It was the buzz around City Hall: DeStefano wants an Obama Cabinet position.

City officials and aldermen have said throughout the year that they think DeStefano would quickly accept a position in the White House if Illinois Sen. Barack Obama wins the presidency and taps him for a one. In fact, at a Yale College Democrats meeting in September, he said he wanted to “see what happened in the national election” before determining whether to stay as mayor for the long run. And in a rare move for mayors, DeStefano went out of his way to formally endorse the Illinois junior senator before the Connecticut primary.

“If Barack Obama wins the election, [DeStefano] will be persuaded to join his cabinet,” an upper-level city official, who asked to remain anonymous in order to freely discuss the mayor’s plans, said yesterday.

But DeStefano — who brought the city national attention when he first announced plans for the Elm City Resident Card in 2007 — said he does not expect to leave New Haven for Washington.

“I’d take ambassador of Italy,” he said. “But short of that — not interested.”

On Monday, DeStefano announced he will run for mayoral re-election. In an interview with the New Haven Advocate that day for a profile on new New Haven Police Department Chief James Lewis, he told associate editor Betsy Yagla that he is running for re-election so that he can see through the end of the chief’s term. Lewis’ term expires January 2010, after DeStefano’s eighth term ends.

DeStefano said in an exclusive interview with the News on Tuesday that he had simply “articulate[d] the closure in my head” about running again. Although he could not point to a precise time when he made the decision, another upper-level city official told the News on Tuesday that the mayor told him his decision “several months ago.”

Yet the rumors about his interest for a more far-reaching government position in the country are not unfounded. After all, he wanted to be governor once.

In 2006, DeStefano ran against Republican Gov. M. Jodi Rell as the Democratic candidate. City officials decried the mayor at the time for not paying attention to the city enough during his venture for state official.

When asked whether he would consider running for governor in 2012, DeStefano skirted around giving a definitive answer: “If I thought there was a compelling reason and I thought it’d hold value, sure I’d consider it, but I don’t see it as a matter to consider right now.”

But for now, he will focus on New Haven — and on Nov. 3, 2009.

“I’m really enjoying this job … that I do know will end someday,” he said at the end of the interview, before heading over to the city’s new Obama headquarters on Chapel and Church streets to watch the presidential debates.