A source familiar with the dispute told reporters last night that Elon Musk and Twitter were close to reaching an agreement to halt their litigation and clear the way for Musk to finish his $44bn bid for the social media network.

Mr. Musk, who is also the chief executive officer of electric vehicle manufacturer Tesla Inc, proposed late Monday to Twitter that he would reverse course and honor his April deal to purchase the company for $54.20 per share provided Twitter dismissed its lawsuit against him.

Musk's Monday proposal stipulated that the closure of the acquisition was contingent upon the receiving of the requisite debt finance.

According to the source, who requested anonymity because the conversations are private, the possible agreement would probably eliminate this restriction.

Tuesday, Twitter's legal team and Musk's legal team informed the judge of their efforts to overcome mutual mistrust and find a way to close the deal.

Wednesday's closing price of $51.63 for Twitter shares was a decrease of 0.7%.

The stock reached its highest level since April when Musk and Twitter agreed that he would purchase the firm for $54.20 a share.

Musk announced in July that he was withdrawing from the deal after discovering, among other allegations, that Twitter had misled him about the number of phony accounts.

Musk is due to testify under oath in Austin, Texas in a case based on charges made public in August by Twitter whistleblower Peiter 'Mudge' Zatko.

Twitter's legal team wished to explore whether Musk's attorney, Alex Spiro, had interacted with the whistleblower as early as May.

The law firm's attorneys denied having any contact with Zatko or his representatives.

Spiro did not reply to a request for comment immediately.

According to court records, Twitter discovered an anonymous email sent to Spiro on May 6 by "a former Twitter executive who led teams directly responsible for trust & safety/content moderation."

The sender provided alternative communication methods.

Zatko, who served as Twitter's head of security until his dismissal in January, has testified under oath that he did not speak with Musk or his attorneys.

The judge, Delaware Court of Chancery Chancellor Kathaleen McCormick, ruled on Monday that it is "at least plausible" that Zatko sent the anonymous email.