The price tag could end up at $60 billion, equivalent to 550 billion kronor, Dagens Industri reports.
In a financing round last year, Anysphere was valued at approximately SEK 275 billion, according to the newspaper.
San Francisco-based Anysphere has developed the AI assistant Cursor, which helps programmers with natural-language commands.
The SpaceX option to purchase Anysphere is not binding.
