President-elect Donald Trump is considering choosing Florida Gov. Ron DeSantis as his nominee for defense secretary to replace the embattled Fox News host Pete Hegseththree sources familiar with the transition told CBS News on Tuesday evening.

This came after Trump and DeSantis attended a memorial service for fallen police officers in Florida on Tuesday.

The Wall Street Journal was the first to report this story.

On Capitol Hill Wednesday morning, Hegseth told CBS News that he does not plan to withdraw his name from consideration. Hegseth said he spoke to Trump on Wednesday morning and Trump told him to move on.

“I spoke to the president-elect this morning. He said, ‘Keep going, keep fighting. I’m behind you all the way,'” Hegseth said. “Why should I back out? I’ve always been a fighter. I’m here for the fighters. This is personal and passionate to me.”

A spokesman for DeSantis had no comment when reached by CBS News. A spokesman for Trump also declined to say whether DeSantis was being considered.

The change comes as Hegseth faced a series of negative stories about allegations of sexual misconduct. Financial Mismanagement at Veterans Charitiesrepeated intoxication and infidelity. Hegseth met with Senate Republicans on Capitol Hill this week to try to drum up support ahead of his confirmation hearings.

At least four Republican senators would likely withhold their support for Hegseth if a vote were held today, two sources familiar with the situation told CBS News.

“Some of these articles are very disturbing. He obviously has a chance to defend himself here, but some of it will be difficult,” Republican Sen. Lindsey Graham of South Carolina told reporters on Tuesday. “Time will tell.”

Republican Sen. John Kennedy of Louisiana, who said he had also read the coverage and was aware of the allegations, said Hegseth needed to address them.

“I want to know if they’re true and I want to hear his side of the story and he’s going to have to address them,” he said Tuesday, adding that he wasn’t sure whether Hegseth’s nomination would face headwinds.

On Monday, The New Yorker reported that Hegseth, before becoming a full-time anchor at Fox News, was forced to resign from two nonprofit advocacy groups – Veterans for Freedom and Concerned Veterans for America – amid complaints about his alleged behavior, which included repeated abuse included being drunk on the job, maintaining a hostile work environment and mismanaging charity funds. CBS News reported that Jessie Jane Duff, a Marine veteran who served as one of Trump’s 2024 campaign managers, was among those who pushed to oust him from Concerned Veterans for America in 2016.

A lawyer for Hegseth has denied the allegations.

DeSantis ran unsuccessfully for the Republican presidential nomination against Trump before dropping his bid in January after disappointing results in the Iowa and New Hampshire primaries. He supported Trump at the time, despite their hostile campaigns. In April the two men privately at DeSantis’ request at a golf club in Florida.

Donors and advisers to both Trump and DeSantis are pushing for detente between the two, which they say is in the best interest of the Republican Party, according to a senior Trump adviser.

DeSantis was commissioned into the U.S. Navy as a JAG officer while attending Harvard Law School. He later served in Iraq, for which he was awarded a Bronze Star.