Donald Trump’s nominee for defence secretary says “the Left” is trying to smear him with “fake” stories – after reports suggested the US president-elect may replace him.

Trump is considering replacing Pete Hegseth with Florida Governor Ron DeSantis, the BBC’s partner CBS News reported, after Hegseth’s nomination came under intense scrutiny.

Since Trump nominated the former Fox News host, questions about Hegseth’s qualifications have been raised – and a historical sexual assault allegation has surfaced.

Hegseth has denied any wrongdoing, and was never arrested or charged.

His nomination is the subject of growing scrutiny by members of his own party – including US senators who have the power to confirm or deny his appointment when are asked to vote on it.

“I think some of these articles are very disturbing,” Senator Lindsey Graham told CBS on Tuesday. “He obviously has a chance to defend himself here, but some of this stuff is going to be difficult.”

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

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

The latest speculation – first reported by the Wall Street Journal – comes as Hegseth meets members of Congress this week to discuss the job 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 does not 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 quoted in the complaint said that Hegseth, then a Fox host, took her phone and blocked the door to a hotel room while at a Republican conference in California.

Hegseth denies any wrongdoing, saying the encounter was consensual.

Some of Hegseth’s past comments about how he might change the defence department have also raised 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 this practice had not made the military “more effective” or “more lethal”.

There is increasing scepticism about Hegseth’s chances of getting enough votes to be confirmed by the Senate, CBS reports.

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

Republicans are expected to have a 53-seat majority in the Senate, which must confirm cabinet-level positions in Trump’s new team. Losing four Republican votes would be enough to sink Hegseth’s nomination, provided Democrats and independents also vote against him.

Some Washington lawmakers have questioned Hegseth’s credentials for overseeing the complex bureaucracy in the job for which he has been lined up.

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

John Bolton, who served as national security adviser during Trump’s first presidency, 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?” Bolton asked.

Hegseth is not Trump’s first controversial appointment before he returns to the White House.

Former Florida Congressman Matt Gaetz, who Trump nominated for US attorney general, also faced scrutiny over allegations of sexual misconduct against him – which he denied – that were the subject of a congressional report.

Gaetz eventually withdrew his nomination in late November, saying that the controversy against him “was unfairly becoming a distraction” from the work of the incoming Trump administration.

North America correspondent Anthony Zurcher makes sense of US politics in his twice weekly US Election Unspun newsletter. Readers in the UK can sign up here. Those outside the UK can sign up here.