The network is used by the Ukrainian military, sources say, and Trump says "if there is a problem, I'll get it straightened out".
Musk says there's "a lot to be gained" by combining the firms in what would be the biggest merger in history.
Musk says special committees within both companies have been formed to look at a possible mega-merger.
Musk's announcement comes after Anthropic pledged to create a public benefit fund ahead of its blockbuster stock market listing.
New filings show the world's richest person spent this summer again trying to help Republicans win office, with most of his focus on one candidate.
Speed curbs limited Ukraine's defences against deadly Russian attacks on Tuesday night.
A new version of Tesla's Roadster electric sports car, equipped with thrusters which apparently allow it to hover and turn in mid-air, has been unveiled in Texas.
Tesla CEO Elon Musk showcased the vehicle at a facility owned by his SpaceX company, which helped develop the model.
Ukraine's president has told Elon Musk that any restriction on the Starlink's system cost lives.
