His time serving as one of Trump’s top advisers has frustrated some Cabinet ministers who have privately accused him of overreach.
By his own admission, Musk has taken a chainsaw to the federal workforce since arriving in Washington, resulting in mass firings and the shutdown of entire government departments.
The President, however, remains pleased with Musk despite frustration from those closest to him and he is likely to retain an informal role and an adviser, according to Politico.
The transition is likely to coincide with the end of his designation as “special government employee”, which limits him to 130 days of service during a one-year period.
On Monday, Trump hinted that would have to go back to running his companies fulltime saying: “He’s got a big company to run... At some point he’s going to be going back.”
“He wants to. I’d keep him as long as I could keep him,” he added.
The de facto head of Doge, sitting alongside his aides, told Fox News’ Bret Baier last week that he expected to accomplish “most of the work required to reduce the deficit by $1 trillion” within the 130-day timeframe.
Musk, who was at the centre of a fiery Cabinet showdown earlier this month, was given a seat at Trump’s Cabinet meeting table for the first time last week.
The scene was of stark contrast to last month’s meeting, in which the Telegraph revealed Musk was branded a “liar” by Cabinet members.
Sean Duffy, the Transport Secretary, was enraged by Musk’s attempts to cull air traffic controllers despite the national shortage.
While the President watched on, Doug Collins, the Secretary of Veterans Affairs, claimed operations were being cancelled in Veteran Affairs hospitals because of Musk’s Doge cuts.
Musk was left humiliated on Monday when the Republican nominee for a Wisconsin Supreme Court seat, whose campaign he funded, lost to the Democratic challenger.
Susan Crawford overcame criticism by Trump and a $21 million (£16 million) donation to her Republican opponent by Musk.
Her victory is a boost for the Democrats, who had framed the race around the popularity of Trump and Musk.
During the campaign, Musk said the race could “decide the future of America and Western civilisation”.