Elon Musk has made an offer to buy Twitter with a bid that values the company at $43.4bn, a move that could turn the Tesla chief executive into a social media mogul.

Musk’s offer of $54.20 a share comes days after he took a 9 per cent stake in the company, becoming its largest shareholder but rejecting an invitation to join its board.

The entrepreneur announced the offer on Thursday in a filing with the US Securities and Exchange Commission.

The filing said the $54.20 a share offer was a 38 per cent premium to the share price on April 1, the day before his share purchases became public.

This story is developing . . .