It may have seemed like a publicity stunt at one point, but now it is getting serious.
According to a report by The New York Times, sources with knowledge of the situation say that the board is close to a deal to sell itself to Musk. The negotiations went into the early hours of Monday, according to sources.
The key moment in the negotiations was Musk announcing in a SEC filing last week that he has secured $46.5 billion in financing to acquire the company.
The report claims that the deal may still fall apart.
By early April, Musk had amassed a 9.2 percent stake in the company. He started questioning the policies of the service a few days before he made the announcement.
At one point, it appeared that Musk was going to become a member of the Board of Directors of the company, and then he was going to buy the entire company for $54.20 per share.
Reactions to Musk's bid were mixed. There were, of course, meme. Some Wall Street analysts thought that Musk's bid price was too low. Musk has recently praised Jack Dorsey for his new title at his other company, Block, and seems to still be on good terms with him.