Musk, who is also chief executive officer of electric car maker Tesla Inc, proposed to Twitter late on Monday he would change course and abide by his April agreement to buy the company for $US54.20 ($A83.16) per share, if Twitter dropped its litigation against him.

In their effort to end the litigation, the two sides agreed to postpone the billionaire's deposition in court scheduled for Thursday, the source said on Wednesday, but negotiations are continuing with a full resolution expected to take more time.

However, Twitter's legal team was yet to accept any agreement and Chancellor Kathaleen McCormick, the judge on Delaware's Court of Chancery, earlier in the day said she was preparing for the looming trial.

"The parties have not filed a stipulation to stay this action, nor has any party moved for a stay. I, therefore, continue to press on toward our trial set to begin on October 17, 2022," McCormick wrote in a Wednesday court filing.

Musk's proposal on Monday included a condition that the deal closing was pending the receipt of debt financing. The potential agreement would likely remove that condition, said the source, who requested anonymity as the discussions are confidential.

Twitter's legal team and lawyers for Musk updated the judge on Tuesday with their attempts to overcome mutual distrust and find a process for closing the deal.

Two firms that were interested in partly financing the deal, Apollo Global Management Inc and Sixth Street Partners, had ended talks to provide up to a combined $US1 billion ($A1.5 billion), two sources told Reuters.

A lawyer representing a proposed class action against Musk on behalf of Twitter shareholders said in a letter to McCormick that Musk should be required to make a "substantial deposit" in case he again reneges on his commitment to close.

He should also be liable for interest delaying the closing of the deal, said the letter from lawyer Michael Hanrahan.

Representatives of Musk and Twitter held several unsuccessful talks in recent weeks about a possible price cut to his $US44 billion ($A68 billion) deal to buy the social media platform before he reversed course on Monday, the New York Times reported on Wednesday.

Musk initially sought a discount of as much as 30 per cent, according to the report, which was later narrowed to about 10 per cent and ultimately rejected by Twitter.

It is not clear what led the Musk legal team to offer to settle, but his scheduled deposition on Thursday in Austin, Texas, was expected to include some tough questioning, which could have given Twitter leverage in talks to close the deal.

Shares of Twitter closed 1.3 per cent lower at $US51.30 ($A78.71) on Wednesday. The stock on Tuesday hit its highest level since Musk and Twitter agreed in April that he would buy the company for $US54.20 ($A83.16) per share.

Musk said in July he was walking away from the takeover agreement because he discovered Twitter had allegedly misled him about the amount of fake accounts, among other claims.

Australian Associated Press