President-elect Donald Trump is considering naming Florida Governor Ron DeSantis as his pick for defence secretary, replacing Pete Hegseth, whose nomination has come under intense scrutiny, according to the BBC's news partner CBS.

Since Trump nominated Hegseth, a former Fox News host, to lead the US Department of Defence, a sexual assault allegation has surfaced, as well as questions about his qualifications.

The Wall Street Journal was first to report this story.

DeSantis ran against Trump in the Republican primary and before dropping out, he was considered by some to Trump 2.0, a Republican who could deliver Trump's populist agenda without baggage.

DeSantis, who was elected as Florida governor in 2018, did not reply to a request for comment and a spokesperson for Trump declined to say whether DeSantis was under consideration for the post, CBS reported.

The news comes as Hegseth, whose nomination was announced in mid-November, meets with members of Congress this week to discuss the job, which requires Senate approval, and drum up support.

A graduate of Princeton and Harvard universities, Hegseth was an infantry platoon leader in Guantanamo Bay and Iraq, and was awarded the Bronze Star Medal.

In nominating Hegseth, who is also a former Fox News TV host, Trump highlighted the former soldier's education, and his military experience in Afghanistan and Iraq. "With Pete at the helm, America’s enemies are on notice - our military will be great again, and America will never back down," Trump wrote.

But even as a veteran of the wars in Afghanistan and Iraq, the 44-year-old doesn't have the extensive experience typical for the cabinet position. He also would be the second-youngest person to serve in the office.

In addition, since his nomination, a police report detailing accusations of an alleged sexual assault in 2017 has surfaced.

The woman said that Hegseth, then a Fox News host, took her phone and blocked the door to a hotel room while at a Republican conference in California, according to the report.

Hegseth has denied any wrongdoing and claims the encounter was consensual. He was never arrested or charged.

The 22-page report on the investigation includes interviews with the victim, a hotel staffer, a nurse and a witness who was at the hotel at the time of the alleged incident.

Some of Hegseth's past comments about how he might change the department if confirmed also have raised some eyebrows.

On a recent podcast, Hegseth said the chairman of the joint chiefs of staff - the top military leader in the US - should be fired, along with any military leader "involved in any of the DEI [diversity, equity and inclusion] woke [expletive]”.

He also has argued that women should not serve in combat roles because it had not made the military "more effective" or "more lethal".

According to CBS, there is increasing skepticism about Hegseth's chances of getting enough votes to be confirmed by the Senate.

At least four Republican senators would be likely to vote against him if they voted today, two sources told CBS News.

Republicans are expected to have a 53-seat majority in the Senate, which must confirm cabinet positions. Losing four Republican votes and all Democratic votes would sink Hegseth's nomination.

Some Washington lawmakers initially were surprised by Hegseth's nomination to oversee the complex bureaucracy.

“I confess I didn’t know who he was until 20 minutes ago,” Representative Adam Smith, top Democrat on the House Armed Services Committee, said. “And he certainly doesn’t seem to have any background whatsoever in (Department of Defence) policy.”

John Bolton, who served as Trump's national security adviser, told the BBC that the post of defence secretary should never be a "loyalty appointment".

"The question is: Will he be a yes man to Donald Trump or will he behave professionally and with courage the way he did when he was in uniform?" added Bolton.

Born in Minneapolis, Minnesota, Hegseth lives with his wife and seven children in Tennessee.