US President-elect Donald Trump has a number of contenders for the highly sought after position of secretary of state - including Rudy Giuliani, Mitt Romney and, now, ex-CIA chief David Petraeus.

The retired general met with Trump on Monday (28 November) for about an hour, Petraeus told reporters following the sit-down meeting. "He basically walked us around the world, showed a great grasp of a variety of the challenges that are out there and some of the opportunities as well. Very good conversation, and we'll see where it goes from here," he added.

Trump was equally impressed, he noted in a tweet. The president-elect is set to meet with another secretary of state hopeful, Senator Bob Corker of Tennessee, on Tuesday, The New York Times reported. Corker, chairman of the Foreign Relations Committee, will meet him in Trump Tower, where Trump has been camped out during the transition period.

The president-elect is scheduled to meet Romney, the former GOP presidential nominee, for a second time on Tuesday night. The Times reported that Romney is Vice President-elect Mike Pence's preferred choice for the position.

However, Romney is a contentious figure within the Trump team. Senior adviser Kellyanne Conway has openly criticised Romney for his comments against Trump during the election campaign and questioned whether he had the experience to take up the job.

David Petraeus
Former CIA director David Petraeus speaks to the media after a meeting with US President-elect Donald Trump at Trump Tower in New York, US, 28 November 2016.REUTERS/Lucas Jackson

"The number of people who feel betrayed to think that Governor Romney would get the most prominent Cabinet post, after he went so far out of his way to hurt Donald Trump — there was the Never Trump movement, and then there was Mitt Romney," Conway said to CNN. According to MSNBC's Morning Joe, the president-elect was "furious" after Conway went rogue with her comments.

However, Petraeus brings his own problems to his potential nomination. He was forced to resign as CIA chief in 2012 after admitting he shared classified information during an extramarital affair. In July, FBI Director James Comey testified that Petraeus had lied to agents during the investigation. He was sentenced to two years' probation and a $100,000 (£80,537) fine in 2015.

NBC News has reported that former US Ambassador to the United Nations John Bolton is also under consideration for the post.