Elon Musk has proposed to go ahead with his original offer of 54.20 U.S. dollars per share to purchase Twitter, reversing his attempts to back out of the deal.

Sources familiar with the matter confirmed the development, sending the social media giant's shares up by as much as 15 percent on Tuesday.

Bloomberg reported the development earlier, noting that the billionaire made the proposal in a letter to Twitter. The report cited people who asked not to be identified discussing confidential information.

Twitter's board unanimously agreed to sell the platform to Musk for 44 billion U.S. dollars in April.

Soon after, he tried to back out of the deal, officially informing the company in July of his intentions to terminate the agreement.

Twitter responded by suing Musk to force him to go through with the purchase.

The latest twist comes as the two sides were preparing to go to trial in Delaware Chancery Court on October 17.

CNBC reported that Musk could own Twitter within a matter of days and that all litigation would come to an end.

(With input from agencies)