The US president-elect had selected former Fox News host Pete Hegseth to lead the Pentagon, but there is speculation that he would fail a Senate vote.
Donald Trump’s pick for defence secretary has pledged to carry on and said he still has the president-elect’s backing amid reports he could be replaced.
Mr Trump was said to be considering ditching Pete Hegseth in favour of Florida governor Ron DeSantis.
There are doubts Mr Hegseth could clear the Senate vote required due to claims about his personal and professional life.
On Wednesday, he met Republican senators whose vote he will need to be confirmed, and in a clip posted on X told a CBS News reporter he still had Mr Trump’s backing.
He said: “I spoke to the president-elect this morning. He said ‘keep going, keep fighting’… Why would I back down? I’ve always been a fighter. I’m here for the warfighters. This is personal and passionate for me.”
Mr Trump’s picks for his cabinet have attracted controversy and there has been speculation some might struggle to be confirmed.
Matt Gaetz, his initial pick for attorney general, has already withdrawn from the process.
Two sources familiar with the decision-making told Sky News’ US partner network NBC News that DeSantis, once a rival in the Republican presidential race, could be chosen to replace Mr Hegseth.
Mr DeSantis is “very much in contention”, according to one source.
NBC News reported Mr Hegseth’s nomination was in jeopardy after at least six Republican senators were wavering in their support.