According to the publication, the lawsuit was filed by the company in a Delaware court.
The court will determine whether Musk had the right to unilaterally declare the termination of the deal to merge with Twitter.
Earlier, Elon Musk notified Twitter of the termination of the deal to buy the company due to the fact that the social network did not fulfill contractual obligations.
Twitter Chairman Bret Taylor announced plans to sue the American businessman.