The board of the social media giant is reported to have met with Mr Musk over the weekend to discuss his $43bn offer.
Twitter had initially rebuffed the billionaire’s approach.
But according to reports, Twitter is now in the final stages of negotiations with Mr Musk to buy the business.
Reuters, the news agency, reported that an announcement may come later on Monday after Twitter’s board met and recommended a deal to its shareholders.
Shares rose almost 4% to $50.62 on the reports, but remained below Mr Musk’s offer price of $54.20 a share.
Mr Musk’s targeting of Twitter has moved at remarkable speed. It emerged at the beginning of April that Mr Musk, who is the boss of electric carmaker Tesla, had become the largest shareholder in Twitter with a 9.2% stake.
He was then invited to join Twitter’s board but turned down the offer before launching a surprise bid for the company on 14 April, saying he wanted to “unlock” the social media platform’s “extraordinary potential”.
Twitter responded by putting in place a so-called “poison pill” defence to fend off Mr Musk. The mechanism would have created difficulties for Mr Musk if he attempted to increase his stake in the company.
The board now appears to have U-turned after Mr Musk revealed he had lined up a $46.5bn financing package for his offer – with funding from a mixture of his own assets and the backing of Wall Street banking giant Morgan Stanley and other firms.
Mr Musk recently said that he believes that Twitter should be more open and transparent. “I think it’s very important for there to be an inclusive arena for free speech,” he told the TED2022 conference in Vancouver.
The billionaire, who is the world’s richest man according to Forbes magazine, has also hinted at his plans for Twitter.
He asked his 83.3 million followers on Twitter if the social media platform should allow people to edit their posts – 74% of those who responded wanted an edit button.
Mr Musk’s has also criticised Twitter’s process of verifying a Twitter account which he said was like “if Kafka had a Magic 8-Ball!”.
Even Twitter itself didn’t appear to take Elon Musk seriously when he first said that he wanted to buy it. It’s just Musk being, well, Musk, everyone thought. He may be the world’s richest man but he is also by his own admission cash-poor – and he is well-versed in posting unsubstantiated grand ideas on social media.
But underestimate him at your peril. He is a multi-billionaire and Twitter is one of his favourite toys – so he’s come back with a funded $43bn offer that the firm’s shareholders are now looking likely to accept.
Twitter hasn’t explicitly explained why it didn’t initially want to become part of Mr Musk’s empire. Certainly any social media firm with regulators breathing down their necks is going to be wary of a new owner who wants to “open up” the platform to more freedom of speech and less moderation.
He’s also keen on subscription rather than advertising as a business model, which may prove a hard sell for a platform that has not experienced significant user growth in ages.
A Musk-owned Twitter would have a very different feel, for sure. But he also brings to it his own brand of magic -criticise him on social media and you’ll soon bear the brunt of devoted fans who idolise him.
Twitter may decide to try to find an alternative buyer but Musk’s star quality would be difficult to substitute.
He also recently tweeted: “If our Twitter bid succeeds, we will defeat the spam bots or die trying”…..And authenticate all real humans.”
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