Marco Rubio Wants to Be Trump’s Vice President. He Doesn’t Want to Audition.

Senator Marco Rubio, the Republican of Florida, has not visited the courthouse in Manhattan to flaunt his support for Donald J. Trump like other potential running mates. He is not a fixture at the former president’s campaign rallies and has not become part of the furniture at Mar-a-Lago, like other Republicans craving relevancy.

Instead, Mr. Rubio has taken a low-key approach in aiming to become the next Republican vice-presidential nominee, a strategy with a clear logic: Mr. Trump is known to bristle when anyone gets too close to his limelight.

But for Mr. Rubio, it’s also a strategy with a history. When the two men competed for the Republican nomination in 2016, Mr. Trump relentlessly mocked his rival’s height, his ears and his mannerisms. Mr. Rubio hurled his own schoolyard taunts, which landed awkwardly and then backfired painfully until his defeat. Since then, the senator has been careful and discreet about how close he gets to Mr. Trump.

His behind-the-scenes maneuvering has transformed him from bitter rival to occasional policy adviser and, now, a leading contender to join Mr. Trump’s ticket, advisers to the former president said.

The son of Cuban immigrants, Mr. Rubio could help Mr. Trump appeal to Hispanic voters. Now more of a seasoned politician than the youthful “Republican savior” on the 2013 cover of Time, Mr. Rubio might also reassure Republican donors and the moderate voters who backed former Gov. Nikki Haley of South Carolina over Mr. Trump in the primary. (Notably, Ms. Haley endorsed Mr. Rubio’s presidential bid in 2016.)

Trump aides and donors also view the senator as one of several candidates who would pose little risk of creating unwanted distractions for a candidate already facing multiple legal threats. He is also known to have a strong relationship with Susie Wiles, a fellow Floridian and Trump campaign senior adviser who is coordinating the search for a running mate.