According to a report from the New York Times, both sides were discussing details including a timeline and fees if an agreement was signed and then fell apart. The people said the situation was fluid and fast-moving.
Twitter had enacted an anti-takeover measure known as a poison pill that could make a takeover attempt prohibitively expensive. But the board decided to negotiate after Musk updated his proposal to show he had secured financing, according to The Wall Street Journal, which was first to report the negotiations were underway.
On 14 April, Musk announced an offer to buy the social media platform for $54.20 per share, or about $43 billion, but did not say at the time how he would finance the acquisition.
Last week, he said in documents filed with US securities regulators that the money would come from Morgan Stanley and other banks, some of it secured by his huge stake in the electric car maker.
Neither Twitter nor Mr Musk replied to a request for comment from The Independent before time of publication.
Mr Musk has said he wants to buy Twitter because he does not feel that it is living up to its potential as a platform for free speech.
In recent weeks, he has voiced a number of proposed changes for the company, from relaxing its content restrictions — such as the rules that suspended former President Donald Trump’s account — to ridding the platform of its problems with fake and automated accounts.
Mr Musk is the world’s wealthiest person, according to Forbes, with a nearly $279 billion fortune. But much of his money is tied up in Tesla stock — he owns about 17 per cent of the company, according to FactSet, which is valued at more than $1 trillion — and SpaceX, his privately held space company.
It is unclear how much cash Mr Musk has, but a regulatory finding to the US Securities and Exchange Commission suggests that he does have the funding to purchase Twitter – pushing back against doubts that stem from his ‘funding secured’ tweet sent in 2018 to take Tesla private, and which resulted in a $20 million fine from the SEC.
Reuters has also reported similar discussions, with the Twitter board debating whether the sale could be made on more attractive terms. Twitter shareholders apparently urged the board not to let the opportunity for a deal slip away. The board apparently wants to know if there are any more active investigations into Mr Musk from regulators like the SEC that could stop the deal falling through.
If it was established that Mr Musk buying the company would be too great a risk, there could be a break-up fee for Twitter.
Additional reporting by Associated Press.