Maybe it’s the beard, the persistent, salt-and-pepper whiskers, always trimmed to a perfect length that makes Patrick Mouratoglou initially seem more like a French existentialist philosopher rather than tennis coach.

Or maybe he is a tennis venture capitalist. Or a tennis resort executive. Or a tennis “guru,” as Stefanos Tsitsipas, the Greek star, has referred to him. Depending on the moment, Mouratoglou can be all of those things, which can make it difficult for him to also be a coach, at least in the way he thinks a professional tennis coach should coach. That may seem odd for a man best known as one, a man who wrote a book about himself called “The Coach,” but it is the way he always intended it to be.

For years, Mouratoglou has been courtside at Serena Williams’s matches. He has coached her since 2012, and was presumed to be her boyfriend for a time. Coaching her from the stands during the 2018 U.S. Open final led to one of the most notorious meltdowns of Williams’s career. She is not at the U.S. Open this year, having withdrawn to recover from a hamstring injury.

Mouratoglou, though, has been everywhere, just as he is at every major tennis tournament these days.

There he is sitting a seat away from Tsitsipas’s father and coach, Apostolos, during early-round matches against Andy Murray and Carlos Alcaraz. After a match, he grabs a microphone for one of any number of television interviews he does about the state of the modern game. Sometimes he camps out in the plaza of the U.S.T.A. Billie Jean King National Tennis Center and signs autographs for fans who know him better than they know most of the players. Last Tuesday night, he passed a sports drink onto the court of Arthur Ashe Stadium, trying to help relieve the cramps of Holger Rune, the 18-year-old Danish player who trains at his academy, as Rune fell in four sets to Novak Djokovic in the first round.

At age 51, Mouratoglou has become one of the most recognizable stars in tennis, even though he was never more than a middle-rung junior player as a teenager in France. Corey Gauff, the father and coach of the rising American star Coco Gauff, often wears a baseball hat with Mouratoglou’s “M” logo above the brim when he watches his daughter play.

He is the rare coach who has turned himself into a brand, which may mean he is better at marketing than he is at coaching. Don’t ask Mouratoglou to boil down his approach to tennis into a simple strategy or formula.

“My philosophy is I know nothing,” he said in an interview days before the start of the U.S. Open. “I learn the person and I learn my player. A lot of coaches start with their method. There is one method per player and I need to find it.”

Tennis is in an odd spot at the moment. The careers of most of its biggest stars are in repose. Its greatest men’s player, Novak Djokovic, is worshiped in his own country but has never been universally embraced. Naomi Osaka is already a tennis megastar, but she has played little this year and announced Friday night that she was going to take another break from the game.

That leaves enough space for a coaching figure like Mouratoglou to fill.

Tennis does this every so often, producing a coach who is a savvy marketer and businessman to become far more than a teacher and trainer, usually with the help of television cameras that pivot to them as they watch their star players. Think of the Australian Harry Hopman in the 1970s and the New Yorker/Floridian Nick Bollettieri in the 1980s and 1990s.

None though, has reached the level of Mouratoglou.

His empire includes the Mouratoglou Academy, in the south of France, which houses 200 student tennis players, many of whom live and attend school and train there full time.

He runs camps for another 4,000 players, including some adults, each year. Next year, he will offer an e-coaching product.

He is also a chief organizer of the Ultimate Tennis Showdown, a made-for-television competition that has included several top players and has introduced a faster scoring system for matches.

There are Mouratoglou tennis centers at resorts in Costa Navarino in Greece and at Jumeirah in Dubai. He is an investor in the tennis media website Tennismajors.com.

With only 24 hours in a day, he recently gave up his gigs as a commentator for ESPN and Eurosport.

He is the full-time coach of just one player, Williams, but helps oversee to varying degrees the training and development of several others, including Tsitsipas, Gauff, Rune, and Alexei Popyrin, the 22-year-old Australian who reached the third round of the U.S. Open.

Having a portfolio as lengthy as Mouratoglou’s would seem to run counter to someone whose authority flows from his stature as a coach and whose philosophy relies on spending enough time with each player to tailor his methods and strategies to the individual. That approach, Mouratoglou said, requires a deep knowledge of each player’s strengths and weaknesses, both mental and physical, as well as their cultural and family background.

The simplest explanation is that Mouratoglou is no longer really a coach, if he ever was one in the first place, with his work for Williams as an exception. But she may not be around for much longer. It’s not a role he ever intended to play. He took it on out of necessity. His vision for his tennis empire was not going to work otherwise.

As a child, Mouratoglou dreamed of becoming a top professional, but his parents told him it would be too risky and would not support the endeavor. He quit tennis at 16, pursued his education, and at 20 went to work for his father, a leading French industrialist and the owner of a major renewable energy company.

When Mouratoglou was 26, his father told him he was ready to become a partner. Mouratoglou told his father he was quitting. He still had a passion for tennis and wanted to build a tennis empire, beginning with an academy for young players.

He partnered with Bob Brett, an Australian coach and a protégé of Harry Hopman. Mouratoglou knew little about coaching and felt he needed a big name to attract players. Then in 2004 Brett quit. Mouratoglou realized if he found another well-known coach to be his partner, the same thing could happen, so he learned how to coach and found some young prospects whose early careers he could help support, like a venture capitalist seeding a start-up company.

His early recruits included Marcos Baghdatis of Cyprus and Anastasia Pavlyuchenkova of Russia. He began working with Williams in 2012, and has used the stature from her unmatched success to build his empire and a new model for the more expansive role a tennis coach might play.

Mouratoglou now operates like the chief executive of a company with a player development division, with each player functioning as a separate unit or product. He has 50 coaches working for him at his academy. The top pro players associated with him — the ones whose televised matches he makes sure to attend — each has someone else who functions as their coach. Most have only limited contact with Mouratoglou on a practice court, though he supervises the team of fitness trainers the players work with. His academy can serve as base camp where they can train.

Mouratoglou first saw Gauff, 17, when she was 10. He established a relationship with her father, who brought Coco to the academy. He first spotted Tsitsipas, now 23, on YouTube when he was just 16.

“Patrick is kind of like the overseer,” Coco Gauff said the other day.

She said Mouratoglou usually speaks to her through her father if he has any specific pointers, so she does not have too many voices in her head. “He also helps with getting the right people on my team, figuring out who and what I need to help me succeed,” she added.

Both Popyrin and Rune, who has had Lars Christensen as his coach since he was 6, said the most important role Mouratoglou has played is providing them an ideal environment for training.

It is a mutually beneficial relationship. The players, who get access to a first-class training center with nearly every possible amenity, are the best marketing devices to attract other aspiring players, who pay for the academy’s array of services, or for tennis enthusiasts, who attend camps at a Mouratoglou tennis center at a resort.

There is probably no better way for Mouratoglou to make sure everyone knows about his connection with these players than taking his customary spot in their boxes during their matches. All Mouratoglou’s current players in the main draw lost during the early rounds, though there are several players with Mouratoglou ties in the junior tournaments this week.

He has one sacrosanct rule when he attends a match: If he starts with one player, he stays to the end, even if another player his company works with is playing on another court. Leaving midway might send a bad message, he said.

It’s also another way of letting the players know if they need anything, Mouratoglou or someone in his growing empire will be there. Popyrin, who has struggled this year and is 73rd in the ATP rankings, said Mouratoglou has lately been a voice of positivity trying to remind him that he can become a top player, perhaps like the third-ranked Tsitsipas, though he added that Mouratoglou usually functions like a tennis Buddha, a sounding board who listens far more than he speaks.

“I vent to him,” Popyrin said. “He lets you speak your mind, and when you speak your mind to him, a lot of the time you get the answer yourself.”