Musk signaled the deal was on track Wednesday by changing his Twitter profile to "Chief Twit" and posting a video of himself walking into the company's California headquarters carrying a sink.
"Let that sink in!" he quipped.
Musk, the world's richest man, has reportedly been lining up financing since Delaware Judge Kathaleen McCormick paused litigation against him by Twitter's current owners on October 6.
"I think on Friday, we'll get an announcement that says that Elon Musk has purchased Twitter," University of California, Berkeley, law professor Adam Badawi told AFP.
If the buyout doesn't close by the end of the business day on Friday, the judge will likely "bring the hammer down" and head quickly to trial, Badawi added.
Musk tried to step back from the Twitter deal soon after his unsolicited offer was accepted, and said in July he was canceling the contract because he was misled by Twitter over the number of fake "bot" accounts -- allegations rejected by the company.
Meanwhile, the negative publicity about "bots" drove down Twitter's stock price - well below the $54.20 per share he had offered in his takeover bid. Some speculated that Musk was seeking to take the shares at a far lower price than first offered.
Twitter, in turn, sought to prove Musk, the head of the Tesla electric vehicle company, was contriving excuses to walk away simply because he changed his mind.
While pitching the deal to investors, Musk said he planned to get rid of nearly three-quarters of Twitter's workers, according to a Washington Post report.
That report came as a shock in the Twitter workplace, where some employees who would prefer not to work for Musk have already left, said a worker who asked to remain anonymous in order to speak more freely.
Musk's stewardship of the site has sparked worry from activists who fear he could open the gates to more abusive and misinforming posts.
He has vowed to dial content moderation back to a bare minimum, and is expected to clear the way for former US president Donald Trump to return to the platform.
The then-president was blocked due to concerns he would ignite more violence like the deadly attack on the Capitol in Washington to overturn his election loss.