He's a decorated military leader lauded by Democrats and Republicans alike for revolutionizing the military's approach to fighting terrorism and insurgencies, and credited with turning the tide in Iraq. Crucially, he could also allow for a compromise amid reports of divisions within the Trump team, with some backing Mitt Romney and others supporting Rudy Giuliani.
Trump tweeted about the meeting immediately afterwards, saying he "was very impressed" with the retired general.
But Petraeus could still face a difficult path to the top diplomatic post.
For one thing, he would potentially be the third general to hold a Trump Cabinet position, a pile up of former military officers in civilian roles that the new White House could well want to avoid.
For another, there's the matter of his misdemeanor
for sharing classified information. It's a record that raises questions about his ability to get a security clearance and to be confirmed -- particularly as the GOP painted Hillary Clinton as unfit for the presidency for her own handling of classified material.
Petraeus' past a problem?
Petraeus resigned as CIA direct in November 2012, was convicted of a misdemeanor in 2015, and is currently on probation for sharing classified information with his biographer and mistress, former Army intelligence officer Paula Broadwell.
Petraeus agreed to a plea deal that saw him sentenced to two years' probation and forced him to pay a $100,000 fine for sharing classified information.
According to court documents, Petraeus admitted removing several so-called black books -- notebooks in which he kept classified and non-classified information from his tenure as the commander of the International Security Assistance Force in Afghanistan -- and giving them to Broadwell.
Prosecutors agreed not to send Petraeus to jail because the classified information was never released to the public or published in the biography that Broadwell wrote.
However, during the campaign Trump largely dismissed Petraeus' issues, saying they were significantly less grave than those of his former rival Hillary Clinton.
Echos of Clinton criticism
The director of the FBI, James Comey, said Clinton had been "extremely careless" in her handling of classified material and her use of a personal email server for official business while she was secretary of state.
Trump said during the campaign that the FBI erred in not prosecuting Clinton, and at the second presidential debate he pledged to set up a special prosecutor to investigate Clinton if elected. Trump has since downplayed that prospect.
"The system is rigged. General Petraeus got in trouble for far less. Very very unfair!," Trump tweeted in July.
Because he admitted to a misdemeanor and not a more serious felony charge, his conviction does not necessarily prevent him from receiving a security clearance.
His being on probation similarly does not bar him from receiving security clearance, according to experts, though they note that it is unusual as investigators typically prefer to wait until such a legal supervisory period is over before granting clearance.
A president's prerogative
And in any case, experts point out, the President has broad authority to grant security clearances -- even to those with legal challenges.
"Ultimately the President has the final say," Sean Bigley, a security clearance lawyer and former government background investigator told CNN.
He noted that the Supreme Court determined in 1988 that the final authority to bestow security clearances lies with the President.
"This court has recognized the government's 'compelling interest' in withholding national security information from unauthorized persons in the course of executive business ... The authority to protect such information falls on the President as head of the executive branch and as commander in chief," Justice Harry Blackmun wrote in the court's decision.
But while Trump has the legal authority to grant a clearance, it remains to be seen if he will be willing to do so.
"I think Trump will have to make a strategic decision whether the optics of the appointment would be something he is willing to accept," Bigley added.
General continues to be sought out
Petraeus, though, has already received an endorsement of sorts from the Obama administration and Congress.
Petraeus' advice and counsel continue to have been sought by both Capitol Hill and the White House.
"Gen. Petraeus is somebody who served for a number of years in Iraq. He commanded a large number of American military personnel in that country," White House spokesman Josh Earnest said in March of 2015, right around the time of Petraeus' court appearance.
"He is, I think, legitimately regarded as an expert, when it comes to the security situation in Iraq. So I think it makes a lot of sense for senior administration officials to, on occasion, consult for him advice," Earnest added, saying that he was not aware of any special precautions taken amid Petraeus' legal issues.
Petraeus also testified on Capitol Hill, appearing before the Senate Armed Services committee in 2015 to discuss the fight against ISIS.
"Gen. Petraeus, we are very interested in your views," Ranking Democrat Sen. Jack Reed of Rhode Island said at the hearing.
A graduate of West Point, Petraeus holds a PhD from Princeton University and is currently serving as the chairman of the Global Institute at the New York-based private equity firm KKR.
Having commanded the international NATO-led coalition in Afghanistan and overseen US military forces in the Middle East, experts note Petraeus has had ample exposure to key relationships with US allies and critical countries in the region.
One former colleague of his described him as a "diplomat in uniform," noting that Petraeus would be more interested in the secretary of state role as opposed to running the Pentagon.