The conservative Drudge Report reported Tuesday that the one-time four-star general, current director of the CIA, is in the running to become Romney's No. 2 — and its source is allegedly a top Democratic fundraiser who claims President Barack Obama himself recently floated the rumour.
"President Obama whispered to a top fundraiser this week that he believes GOP presidential hopeful Mitt Romney wants to name Gen. David Petraeus to the VP slot!" the report read.
It went on to quote the fundraiser as saying: "The president wasn't joking."
The White House issued an immediate denial.
"Such an assertion has never been uttered by the president and, again, be mindful of your sources," White House press secretary Jay Carney told a briefing.
Indeed, the Drudge Report, despite its purported close ties to the Romney campaign, isn't exactly a trusted news outlet when it comes to veep speculation.
A recent Drudge item that had Condoleezza Rice, former secretary of state under George W. Bush, high on Romney's short list was roundly discredited. Drudge was also accused by Democrats of trying to distract attention away from a bad week on the campaign trail for Romney by building buzz about Rice.
Romney's in the midst of another grim stretch of his campaign, facing continuing pressure to release years of his tax returns as polls suggest Obama is pulling ahead of him nationally and in key battleground states.
The presumptive Republican nominee didn't answer reporters when they asked him directly on Tuesday whether he met with Petraeus recently at his summer home in New Hampshire, as alleged by the Drudge Report.
He was also coy in an interview with Fox News when asked for an update on his selection process.
"I'm a week closer than I was a week ago," he said.
Speculation is in overdrive in D.C. about Romney's pick, which Weekly Standard editor Bill Kristol says could come as early as Thursday. Kristol was instrumental four years ago in convincing John McCain to choose Sarah Palin as his running mate, and is considered part of the Republican elite.
Other political observers were poring over the speaking schedule of the upcoming Republican National Convention in Tampa, Fla., for possible clues.
The Republican National Committee has announced several marquee speakers for the convention, and political junkies believe the absences are significant.
Some big Republican names not yet on the schedule? Tim Pawlenty, Rob Portman, Marco Rubio, Kelly Ayotte, Bob McDonnell, Paul Ryan, Bobby Jindal and Chris Christie — all of them considered potential picks.
Petraeus, meantime, who served as the top commander in Iraq and Afghanistan, has repeatedly said he has no interest in ever running for office.
CIA spokesman Preston Golston told U.S. News and World Report on Tuesday that Petraeus "feels very privileged to be able to continue to serve our country in his current position." He added that Petraeus has stated "numerous times before" that he will not seek elected office.
Obama appointed Petraeus — the brains behind the so-called Iraq surge under Bush — as top American commander in Afghanistan in 2010. Petraeus replaced Gen. Stanley McChrystal, who was fired by the president after bad-mouthing top administration officials in an interview with Rolling Stone magazine.
In 2011, Obama tapped Petraeus to be director of the CIA. That appointment was unanimously approved by the U.S. Senate.
To step down from the helm of the powerful CIA to join the Republican ticket and run against the man who gave him the job would be almost unprecedented.
A Petraeus candidacy would also deliver a damaging blow to Obama's re-election campaign since his administration has often lauded Petraeus as one of history's best military strategists. Petraeus is widely credited with turning the Iraq war around.
Christie, the New Jersey governor, has suggested that so much speculation about vice-presidential picks is over-hyped media silliness anyway.
"'No one's saying: 'I'm not sure about this Obama guy but boy, I love (Joe) Biden,'" he told a news conference in New Jersey earlier this week.
"It's the summer; it's a slow news time. This is what occupies people's attention. He or she will have one debate and that's all you'll hear about the (vice presidential contender). … Joe Biden didn’t play a significant role four years ago, and I don't think he'll play any role now."
Nonetheless that hasn't prevented the political press corps from frantically trying to determine who's got the inside track.
As Romney spent the past weekend at his New Hampshire home with his closest advisers, the contents of his grocery cart were scrutinized after he was photographed wheeling it out of a local supermarket.
The New York Times reported the cart contained 12-packs of caffeine-free Diet Coke, Wild Cherry Diet Pepsi and bags that included Greek yogurt.
There was no immediate word Tuesday whether Petraeus is a diet pop-loving yogurt enthusiast.