CIA chief David Petraeus at the New York Stock Exchange last week to ring the Opening Bell on the CIA’s 65th Anniversary. (Spencer Platt/Getty Images)

CIA Director David Petraeus is reported to be maybe “a leading outside candidate” to be the next president of Princeton, the school’s newspaper reported Thursday.

Petraeus, a retired four-star who’s been at the agency for only a year, would replace Princeton’s first woman president, Shirley Tilghman, who announced her surprise departure Saturday, effective in June.

Chatter about his interest in the job, Princetonian news editor Teddy Schleifer reports, began with a joking response in April to a question at a private, “off-the-record” gathering at Princeton’s Ivy Club, when someone asked whether he was thinking about running for president of the United States.

“I am running for president of Princeton,” he joked, as the audience laughed and applauded. Petraeus got a doctorate from the school.

He wasn’t kidding, “three individuals close to Petraeus” told the Princetonian. And there have been newspaper reports of Petraeus’s wanting the job.

The Brookings Institution’s Michael O’Hanlon, a close friend of the CIA chief, told the paper that he’s had about five chats with Petraeus about the Princeton job. “I don’t think it was a complete throwaway line,” O’Hanlon said.

Alas, the timing could be awkward, O’Hanlon said, and Petraeus is fully committed to his current job. But O’Hanlon added that if Obama loses the election, Petraeus might need new work.

Petraeus, through the agency, issued a kinda Shermanesque statement, saying he loves Princeton but, “as it currently stands, however, I am living the dream here at the CIA.”

Of course, things could change in just 40 days. That’s why great generals always prepare for the unexpected.