Mr Musk has referred to the potential effort as the “Department of Government Efficiency,” or DOGE, the name of a meme and cryptocurrency that he has popularised.
The businessman could also benefit from Trump’s presidency through his ownership of SpaceX, which already dominates the business of sending government satellites to space.
With a close ally in the White House, Mr Musk could seek to further capitalise on those government ties.
Mr Musk has criticised rivals including Boeing for the structure of their government contracts, which he says disincentive finishing projects on budget and on time.
SpaceX has also moved into building spy satellites just as the Pentagon and American spy agencies appear poised to invest billions of dollars into them.
Tesla could meanwhile reap gains from an administration that Trump has said would be defined by “the lowest regulatory burden.”
Tesla’s share price jumped by more than 12% on Wednesday following news of Trump’s victory.
Just last month, the US agency in charge of regulating road safety revealed it was probing Tesla’s self-driving software systems.
Mr Musk has also come under fire for allegedly seeking to block Tesla workers from unionising. The United Auto Workers filed unfair labour practice charges against both Trump and Musk after the two talked about Musk supposedly firing striking workers during a conversation on X.
Trump has also pledged to lower taxes on corporations and the wealthy.
That’s another promise Mr Musk is likely hoping he will keep.