There are reports that the company is close to a deal with Musk.
Musk offered to buy the company for about $43 billion. The social media company had adopted a poison pill to ward off a hostile takeover.
After Musk revealed that he had secured $46.5 billion in financing, the social media site became more receptive to a bid.
A source close to the situation told CNBC that the board met Sunday to discuss Musk's financing plan. The board is looking for other offers and the company could provide an update by the time it reports its latest financial results Thursday, if not before, said the person.
The two sides could reach an agreement as soon as Monday. According to The New York Times, the board met with Musk in the early hours of Monday.
It is not clear what a final deal could look like, and an agreement could still fall apart.
This is breaking news. You can check back for updates.