Gov. Ron DeSantis of Florida said on Monday that his wife, Casey DeSantis, would be a formidable candidate if she chose to run for governor next year, a provocative suggestion that came days after President Trump endorsed Representative Byron Donalds as his preferred Republican candidate for the 2026 governor’s race.

Mr. DeSantis did not outright propose that Ms. DeSantis, a former local TV anchor and breast cancer survivor who has never sought public office, enter the race. But his remarks made clear that the ambitious couple, as has long been rumored, considered her a real possibility to succeed him.

“She’s never angled for anything,” Mr. DeSantis told reporters in Tampa. “But I will tell you this: You’re talking about somebody like her. I won by the biggest margin that any Republican’s won a governor’s race here in Florida. She would do better than me.”

Last week, Mr. Trump announced that he would back Mr. Donalds, a longtime ally, for governor. Mr. Donalds, a Republican from Naples, has not yet said whether he is running — no major candidate has — but has been widely expected to do so.

“Run, Byron, run!” Mr. Trump wrote on social media last Thursday, adding that Mr. Donalds would be “a truly great and powerful governor for Florida.” Mr. Donalds told the Conservative Political Action Conference in Maryland on Friday to “stay tuned” regarding his plans.

By offering endorsements or near-endorsements of two Republicans who are not yet in the governor’s race, Mr. Trump and Mr. DeSantis have set up a new proxy fight after the two were rivals in the presidential primary. Mr. Trump crushed Mr. DeSantis in that contest, but Mr. DeSantis, who is 46, could make another White House run in 2028. Fund-raising and media attention for such a campaign could be easier if the term-limited governor, or his wife, were holding some sort of public office.