Mayor Bloomberg has outlined a detailed scenario under which a third-party presidential candidate might jump into the race even while denying he’d be that candidate.

Mr. Bloomberg made the remarks yesterday while being interviewed by his 2001 opponent for the mayoralty, Mark Green, on Air America Radio.

“It’s a daunting task because we do have a two-party system,” Mr. Bloomberg said during the interview, to be aired next week. “There’s a certain percentage of the public who will always vote in the party they are registered in, but we’ve had third-party candidates before.”

“Whether or not the country really wants that I think it’s easy to say today,” he added. “But after the selection process plays out in both the Democratic and Republican parties, we’ll see.”

The interview made for a strange reunion between two old political rivals, who in the 2001 election were at each other’s throats. This time around, things were friendlier, as the two bantered about the past and joked about their role reversals. Mr. Bloomberg is the founder of a worldwide financial news company who likes to remind people that he is not a career politician. Mr. Green, a politician for years, is now the president of Air America, which his brother, Stephen, a real estate developer, recently purchased and saved from bankruptcy.

“Who would have thought you’re here as the media guy and I’m here as the politician?” Mr. Bloomberg said during the 15-minute session in Air America’s Chelsea studio.

Mr. Green said that while Mr. Bloomberg is qualified to be president, the electoral math would make a win an “impossible task.” Mr. Bloomberg is one of about 30 headliners Air America is interviewing for its re-launch next week. Mr. Green said he wanted to conduct the interview personally.

“I have a unique relationship with Mike Bloomberg,” he said. “Freddy Ferrer and I are in a small club.”