WASHINGTON — The increasing likelihood that Senator McCain will win the Republican nomination could keep Mayor Bloomberg on the sidelines in the presidential race this fall, a close ally of both men said yesterday.

“My feeling all along has been that if he ran, it would be because he had a real reason to run, and frankly, he and John McCain have a lot in common,” Senator Lieberman of Connecticut told The New York Sun in a telephone interview. “So if John gets the nomination, I would guess it’s less likely the mayor will run for president.”

“But,” he added, “obviously that’s his decision to make, and I respect it.”

An independent who caucuses with the Democrats, Mr. Lieberman has endorsed Mr. McCain and will make his first campaign appearance in New York City today when he greets volunteers at a phone bank at the headquarters of the Sergeants Benevolent Association in Lower Manhattan. He remains close, however, with Mr. Bloomberg, who helped him secure a hard-fought re-election win in 2006.

Mr. Lieberman hinted that he might support a Bloomberg bid if Mr. McCain loses the Republican race.

“In that case, I hope he’d think about it, because I think he’s up to the job,” he said of the mayor, adding that he is a “great admirer” of him.

Mr. Bloomberg lost another potential top supporter yesterday when Governor Schwarzenegger endorsed Mr. McCain. The California Republican has referred to the mayor as his “soulmate” and embraced his message of nonpartisanship.

The commitment of Messrs. Lieberman and Schwarzenegger to Mr. McCain adds to the sense that a McCain nomination would leave little political space for Mr. Bloomberg. While the Arizona senator initially courted the conservative Republican establishment as he prepared for a second presidential run, he darted back toward his maverick roots following the near-collapse of his campaign last summer.

The move was a bid to woo independent voters in New Hampshire, but it has since carried him to victories in South Carolina and Florida and put him in a decided advantage heading into “Super Tuesday” over his chief remaining rival, Mitt Romney.

Mr. Lieberman will try to help Mr. McCain shore up a victory on February 5 in New York, where he had opened up a double-digit lead even before Mayor Giuliani dropped out of the race and threw his support to the Arizona senator. In endorsing Mr. McCain yesterday in Los Angeles, Mr. Schwarzenegger cited Mr. McCain’s willingness to work with Democrats in a bipartisan fashion.

“Senator McCain has proven over and over again that he is reaching across the aisle in order to get things done,” the governor said. “There are people out there who talk about reaching across the aisle, but he has shown the action over and over again.”

While Mr. McCain is more conservative than Mr. Bloomberg on social issues — he opposes abortion rights and gay marriage — they overlap on others, most notably on the environment. Mr. Bloomberg has made combating global warming a signature issue in his national platform, just as Mr. McCain has pushed Republicans to acknowledge the challenge of climate change while backing federal regulation on carbon emissions through a cap-and-trade program. (Mr. Bloomberg supports a carbon tax to reduce greenhouse gas emissions.)

Mr. Schwarzenegger highlighted Mr. McCain’s environmental advocacy, holding his endorsement event at the factory of a solar-energy company.

Mr. Bloomberg has denied plans for a presidential run countless times over the last year, and he did so again yesterday when asked during an appearance at Google’s New York office. “I am not a candidate, and I’ll stay that way,” he said.