STORY: Twitter has kicked off negotiations with Elon Musk over the Tesla CEO's $43 billion offer to acquire the social networking site.

That's according to sources familiar with the matter, who say the negotiations signal that Twitter is now considering the possibility of selling the company to Musk on more attractive terms.

Twitter had previously adopted a so-called 'poison pill' to defend against the billionaire's effort to buy the company.

Musk threatened to launch a tender offer in response, to get support for his bid from Twitter shareholders.

Sources say Twitter's board grew concerned that many shareholders could back Musk unless it sought to negotiate a deal.

Musk has insisted that Twitter needs to be taken private in order to grow and become a genuine platform for free speech, and has been meeting with shareholders over the past few days.

He says his current Twitter bid is his "best and final" offer - something which sources say has emerged as a hurdle in the deal negotiations.

Representatives for Twitter and Musk did not immediately respond to requests for comment.

Sources have added that the negotiations don't guarantee Twitter will accept Musk's bid of $54.20 per share.

They also say shareholders' price expectations for the deal have diverged based on their differing investment strategies.

Short term-minded investors, including hedge funds, want Twitter to take Musk's offer... and the sources say some are fretting about a recent plunge in the value of tech stocks.

Whereas active, long-term investors, who along with index funds hold the biggest chunk of shares, want a higher price.

Saudi Arabia's Prince Alwaleed bin Talal, a Twitter shareholder, tweeted earlier in April that quote, "I don't believe that the proposed offer by Elon Musk comes close to the intrinsic value of Twitter given its growth prospects."