In a recent appearance at the World Affairs Council of Philadelphia he turned a question about his retirement plans into an opportunity to deny he has political ambitions. An audience member asked if he planned to write a book when he left the Army. He responded by saying he'd feared the politics question.
"The answer is 'no,"' he said - and he didn't mean no book; he meant no race for the White House.
Part of his stock reply to the politics question - even when it is not asked - is to cite lyrics from a Lorrie Morgan country-western song about rejecting an unwanted suitor: "What part of 'no' don't you understand?"
Then he chuckles as if to suggest he is a bit embarrassed by the fuss - fuss sometimes of his own making.
Is he keeping his options open?
As the most popular and widely known general of his generation, Petraeus, 57, is approaching a new juncture in a career that catapulted him to fame when President George W. Bush sent him to Baghdad in early 2007 to carry out a long-shot "surge" strategy that arguably rescued Iraq from collapse.
Ambitious, shrewd, articulate, famously competitive - Petraeus has a three-decade record of accomplishment, a penchant for publicity and a reputation for toughness that sets him apart in today's military. Those qualities explain why he is sometimes talked about as a prospective presidential candidate - and why the talk seems to make him uncomfortable and energized at the same time.
Nearly two decades ago, similar star qualities drove a wave of public speculation about the political prospects for Colin Powell, who declared himself a Republican after he retired from the military in 1993 and was widely touted as a possible challenger to President Bill Clinton in 1996. Powell, the first black Joint Chiefs chairman, declined to run, saying he lacked the passion and commitment.
Many believe Petraeus is the leading candidate to become the next chairman of the Joint Chiefs of Staff, which is the pinnacle of a military career. Another possibility, generally seen as less likely, is that he would be nominated to be the next chief of staff of the Army, succeeding Gen. George Casey.
In late 2008 after returning from Baghdad he began his current assignment as chief of U.S. Central Command, overseeing U.S. military operations in Iraq, Afghanistan, Pakistan and a wide swath of troubled territory stretching across the greater Middle East. It's a broader set of responsibilities than he managed in Iraq, but it has reduced the public spotlight on him - not so much because he's no longer in Baghdad but rather because the Obama White House has wanted him to assume a lower public profile.
It's not clear whether President Barack Obama, who opposed the Iraq surge that made Petraeus famous, would choose Petraeus as Joint Chiefs chairman, who by law is senior military adviser to the president.
Even though the outcome in Iraq is still in doubt, Petraeus is widely seen as its savior, a miracle worker. He recently was introduced at a Washington think tank as "an authentic American hero, a man of remarkable honor and valor," and "one of the finest military minds America has ever produced."
In addition to Powell, there are plenty of other examples in American history of a popular general turning to politics, beginning with George Washington and including Ulysses S. Grant and Dwight D. Eisenhower. Among four-star Army generals who made a failed bid for the White House are Alexander Haig (1988) and Wesley K. Clark (2004).
A Petraeus watcher, Ray DuBois, sees him either becoming the next Joint Chiefs chairman, replacing Adm. Mike Mullen, whose term expires next year, or retiring. He does not see a political future for Petraeus.
"My hunch is that he will appropriately avoid any consideration of an elective political career, and that he would be well advised to dampen any aspiration in that regard," DuBois said in an interview. DuBois is a former senior civilian Army official and adviser to former Defense Secretary Donald H. Rumsfeld.
It is a strongly held consensus in today's military that top leaders like Petraeus are obliged while in uniform to focus fully on their military duties, setting aside any personal ambitions they might pursue after retirement - especially those in positions of wartime command. Petraeus is known to share that view.
DuBois thinks Petraeus is a natural choice to be chairman of the Joint Chiefs, given his extensive wartime experience and proven ability to negotiate the corridors of power on Capitol Hill and across the government. And although there is no formal requirement for rotating the chairmanship among the services, the Army has gone the longest - nine years so far - without having one of its generals at the top.
Petraeus, whose Army career began in 1974 when he graduated from the U.S. Military Academy at West Point, N.Y., has a doctorate in international relations from Princeton University. Coincidentally, in the late 1990s he served as executive assistant to the last Army general to be chairman of the Joint Chiefs, Hugh Shelton.
The ascendancy of Petraeus has come during a period in American military history in which generals have acquired influence well beyond the battlefield. Petraeus and his counterpart commanders in the Pacific, in Europe and in Latin America are regular visitors to the halls of political power in foreign capitals. Some point to the commanders' clout as evidence that U.S. foreign policy has become militarized.
In Petraeus's case, Bush deliberately elevated his Iraq commander to a position of pivotal importance, saying in effect that Petraeus knew best and that the president was just following his general's lead. That reflected a Bush calculation that Petraeus had more credibility on Iraq than did he.
Peter Mansoor, a retired Army colonel who was Petraeus's executive officer in Baghdad during the surge, doubts Petraeus intends to run for president in 2012 but does not rule out the possibility of him considering it later.
"He adamantly states he's not interested in politics," Mansoor said in an interview. "Privately he's never mentioned anything different to me, so I think you have to take him at his word on that, even though no one is really convinced."
In a Petraeus appearance at Georgetown Law Center in January, an audience member raised the matter of the military's role in society, prompting Petraeus to point to the talk about his own political aspirations.
"I've said 'no' about as many different ways as I possibly could. And I truly mean it," he said earnestly. And then he invoked the memory of William T. Sherman, the Civil War general who famously said of his interest in presidential politics: If nominated I will not run, if elected I will not serve.
"I am Shermanesque in my response to those particular questions," Petraeus said.