Trump has entrusted the Tesla CEO with efforts to cut government funding and dismantle various US agencies as a special government employee.
Politico reported that it was a mutual decision for Musk to return to his businesses but no specific date was decided.
Musk or the White House has responded to the report yet.
Shares of some companies, including government contracting companies, rose following the report.
Shares of Musk's Tesla, which were down 2% in early trading after a sharper-than-expected fall in first-quarter deliveries, reversed course and were up 3%, reports said.