In a statement, the firm said: "Once fully deployed, the SpaceX system will pass over virtually all parts of the Earth's surface and therefore, in principle, have the ability to provide ubiquitous global service."
The satellites would orbit the planet at altitudes ranging from 714 to 823 miles (1,150 to 1,325 km). That is above the International Space Station but below geostationary satellites.
Analysis - Jonathan Amos, Science correspondent
SpaceX has talked about its telecoms ambitions for a while.
Now, under a deadline to file interest with the FFC, the company has given a more technical glimpse of its proposal.
Some 4,425 satellites (plus spares), operating in 83 orbital planes, at altitudes ranging from 689 miles to 823 miles (1,110 km to 1,325 km).
It is understood SpaceX has some prototype satellites it will launch next year, but the actual constellation will not see the light of day until the turn of the decade.
