A senior White House official told NBC News, Sky’s US partner network, that the US president had discussed the Tesla and X boss transitioning back to the private sector at a cabinet meeting last month.
Mr Trump is said to have called Mr Musk a “patriot” at the end of the meeting on 24 March, and told the room that “he has never asked me for a thing”.
On Monday in the Oval Office, the president said Mr Musk would at some point be going back to his businesses.
The official said Mr Musk would leave at the end of his 130 days as a special government employee.
That would be 30 May, but it is unclear if the billionaire businessman will indeed leave on that date.
Previously, the White House said that as a temporary organisation, the Department of Government Efficiency (DOGE) would be terminated on 4 July next year – the 250th anniversary of the US.
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It comes days after Mr Musk said some members of his DOGE team were getting death threats on a daily basis.
Mr Musk had drawn criticism over his efforts to downsize the US federal government.
In just weeks, entire agencies were dismantled, and tens of thousands of workers from the 2.3 million federal workforce have been fired or have agreed to leave their jobs.
A number of lawsuits were filed in state and federal courts over cuts recommended by DOGE.
