Caitlyn Jenner, a former Olympian and prominent transgender activist, is exploring a run for governor of California against Gov. Gavin Newsom, a Democrat, who is facing a possible recall election later this year, according to people familiar with her thinking. She is currently leaning toward running if an election is held, the people said.

Ms. Jenner, a longtime Republican, is being advised by Brad Parscale, Donald J. Trump’s former campaign manager, according to a person familiar with their discussions. Mr. Parscale would not manage Ms. Jenner’s campaign but is guiding her on who to hire for key roles.

Ms. Jenner is also said to be working with Caroline Wren, a prominent G.O.P. fund-raiser who was a senior adviser on the Trump presidential campaign last year and whose name was on a permit for events leading up to the Jan. 6 riot at the Capitol. According to Axios, Ms. Wren connected with Ms. Jenner through a Republican nonprofit working on L.G.B.T.Q. issues.

The California secretary of state is expected to announce soon that the Newsom recall effort has officially qualified for an election; the recall organizers say they have exceeded the 1.5 million signatures needed. Such an election would likely be held later in the year.

So far, the effort to replace Mr. Newsom does not appear to mirror the 2003 recall election in California that ousted Gov. Gray Davis, a Democrat, and elected Arnold Schwarzenegger, a Republican. Despite criticism for Mr. Newsom’s handling of the pandemic and other controversies he has faced, a recent poll found that just 40 percent of the state’s voters would support a recall of the governor.

Mr. Newsom is also helped by the fact that no major Democrat has joined the race. While Ms. Jenner has name recognition, she would be a first-time candidate, and the other Republicans expected to run are not seen as likely to get much traction.

If she runs, Ms. Jenner’s past ties to Mr. Trump would likely complicate her bid, given his deep unpopularity in the state. She supported Mr. Trump early on when he ran for president, but rescinded her support in 2018 after his administration repeatedly attacked transgender rights.

Another person with ties to Mr. Trump’s world, Ric Grenell, who served briefly as the Acting Director of National intelligence, is said by Trump allies to be considering a run of his own for the governorship.