General David Petraeus, one of the United States' best-known military officers and former CIA director, has hinted he would serve in President-elect Donald Trump's administration.

Petraeus led U.S. forces in Iraq and Afghanistan before becoming head of the CIA, but quit his post in 2012 after admitting an affair with his biographer, Paula Broadwell.

Now in a radio interview with the BBC, the retired general said he would have to say yes to any fresh offer to serve.

"I've been in a position before where a president has turned to me in the Oval Office in a difficult moment and .... said 'I'm asking you as your president and commander-in-chief to take command of the International Security Assistance Force in Afghanistan'.

"The only response can be 'yes, Mr. President'," he said Wednesday.

Pressed on concerns about Trump's temperament as a leader, Petraeus said although he had never met the President-elect, he had heard positive reviews.

"It's interesting that those who have been talking to him have said, you know, he's very personable, very hospitable, very gracious guy, full of questions and dialogue," he said.

On the prospect of better relations with Russia, Petraeus told the BBC that history suggested Trump stood a better chance for dialogue than President Obama.

"Only Nixon could have gone to China. Anyone else would have been criticized from the right," he said.

"I think that the current president would have been criticized from the right had he tried some of the kinds of outreach that, in fact, President-elect Trump may pursue."

The Wall Street Journal reported last week that Trump was considering General Petraeus for the post of defense secretary. However in a tweet Sunday, the President-elect praised the retired Marine General James "Mad Dog" Mattis after interviewing for the role.