Elon Musk and Twitter Inc (TWTR.N) may reach a deal to end their lawsuit as soon as Wednesday and enable Musk to close his $44 billion deal for the social media platform, a source familiar with the matter told Reuters.

Musk proposed to Twitter late on Monday he would move in a different direction and abide by his April agreement to buy all of Twitter's shares for $54.2 each if the company drops its lawsuit against him.

Musk's proposal on Monday conditioned that the deal closing was pending the receipt of the necessary debt financing. According to the source that requested to remain anonymous, the potential deal would likely remove that condition.

Musk's lawyers and Twitter's legal team informed the judge on Tuesday of their attempts to try to overcome mutual distrust and find a way to close the deal.

Musk is scheduled to testify on Thursday in Austin, Texas.

Shares of Twitter closed down 0.7% at $51.63 on Wednesday afternoon. On Tuesday, the stock hit its highest level since Musk and Twitter agreed that he would buy the company in April.

In July, Musk walked away from his $44 billion buyout deal because of repeated violations of the agreement, as he claimed, adding that Twitter did not provide adequate information on the quantity of spam and false accounts.

Part of Musk's case was based on claims by Twitter whistleblower Peiter Zatko that became public in August.

Twitter's legal team has wanted to look into whether Quinn Emanuel lawyer Alex Spiro, communicated with the whistleblower as early as May. The law firm said in court filings its lawyers did not communicate with Zatko or his representatives.

While Spiro was requested to comment, it did not respond immediately.

According to court documents, Twitter unveiled an anonymous May 6 email to Spiro from "a former Exec at Twitter leading teams directly involving Trust & Safety/Content Moderation," who offered to communicate "via alternate means."

Zatko, better known as "Mudge", who headed Twitter security before being fired in January, denied under oath having communicated with Musk or his attorneys at Quinn Emanuel.

The judge, Chancellor Kathaleen McCormick of Delaware's Court of Chancery, said in a Monday ruling it is "at least plausible" Mudge sent the anonymous email. She ordered Spiro to file a statement with the court clarifying his actions regarding the May 6 email.