The firm already has permission from the US Federal Communications Commission (FCC) to launch up to 12,000 Starlink craft to low Earth orbit.
According to reports, SpaceX recently filed paperwork with the International Telecommunication Union (ITU) for up to 30,000 additional Starlink satellites.
The recent request for permission could take seven years to get clearances before the specified satellites are launched, The Sun reported on Wednesday.
It is not clear how many Starlink satellites SpaceX will actually build and launch.
And there's no guarantee SpaceX will end up launching the already-approved 12,000 satellites. Musk, the company's founder and CEO, said earlier this year that economic viability could come with a constellation of about 1,000 satellites, space.com report added.