Twitter’s shares rose by more than 5% in pre-market trade on speculation the firm could agree a takeover deal with Elon Musk as early as Monday.
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 Mr Musk’s approach.
But according to reports, Twitter is now in the final stages of negotiations with Mr Musk to buy the business.
Share trading in Twitter’s stock, before the US stock market opened, sent the price up 5.1% to $51.57. Although it is still below Mr Musk’s offer price of $54.20 a share.
Reuters, the news agency, reported that an announcement may come later on Monday after the Twitter’s board has met and recommended a deal to its shareholders.
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.
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.