The shrewd and articulate military commander, credited with turning around the Iraq war, will deliver a speech at Saint Anselm College in New Hampshire next week, a traditional staging post in the state where the first presidential primaries are held every four years. Each of the last eight presidents has spoken at the college on their way to victory.
It will be the latest in a series of speaking engagements where the head of the US Central Command region, which covers the Middle East and Central Asia, has veered well into foreign policy discussion and often faced questions about his political ambition.
His stock response is the same as any potential aspirant at this early stage - a flat no. But for someone who professes to have no interest in running for president he has a way of talking about it even when he hasn't been asked directly.
In a recent appearance at the World Affairs Council of Philadelphia Gen Petraeus turned a question about whether or not he planned to write a book upon retiring into an opportunity to deny he had political ambitions. On other occasions he has laughed off the notion of a White House bid in a slightly disingenuous manner.
Colleagues have begun to semi-seriously joke about the issue. At the annual Washington Alfalfa black tie dinner in late January Robert Gates, the Defence Secretary, was heard to remark that Gen Petraeus couldn't make it because "he had an engagement in Iowa", where the first caucuses are held.
"Everybody who knows him or spends time with him has always thought he would have a chance, and he does nothing much to dissuade them," said Steve Clemons, a senior fellow at the New America Foundation and publisher of the Washington Note blog.
"His closest advisers don't deny the logic or the suggestion," added Mr Clemons, who recently attended a diplomatic Washington dinner party where Gen Petraeus wore business attire rather than uniform.
John Feehery, a well-connected Republican strategist, said: "If Petraeus were to run, he would be a serious contender. "His positions on certain issues are not well known, but his leadership ability is well known and respected by the American people."
Aged 57, Gen Petraeus was catapulted to fame when then President George W Bush sent him to Baghdad in early 2007 to carry out the "surge" strategy that helped rescue Iraq from all-out civil war.
He drew up the counter-insurgency strategy that helped transform that conflict and is now being deployed with some encouraging early signs in Afghanistan.
In what is so far considered a weak field to run against President Barack Obama he would bring cast-iron national security credibility. Of the Republican front-runners, Sarah Palin is regarded as too divisive and Mitt Romney has trouble connecting with voters outside of country clubs.
Registered as a Republican, the general has told friends that like many senior military figures he hasn't voted for several elections in a bid to preserve his independence.
But he has also described himself as a "Rockefeller Republican" – a pro-business, socially liberal New Englander – who would not fit in well with a party lurching to the Right under the influence of the new Tea Party movement.
Like Gen Colin Powell or Gen Wesley Clark, who flirted with and entered the political fray respectively, he may lack the stomach for non-stop campaigning and fund-raising.
Timing is also against him for 2012. For a serious bid, he would have to leave his command late this year while the Afghan war was still blazing and then try and run against his former boss, the president.
Some associates think 2016 is a safer bet, or the chairmanship of the Joint Chiefs of Staff, the pinnacle of any military career. There is also conjecture that Mr Obama, who is an admirer, may line him up for a top job if he wins a second four-year term.