Mr Musk posted a video of himself entering the building in San Francisco while carrying a sink - alongside the caption, “Entering Twitter HQ - let that sink in!”
The 51-year-old entrepreneur also changed his Twitter bio to “Chief Twit” and his location to the HQ.
According to reports, a final credit agreement has been put together by banks involved in the takeover, with documentation still to be signed.
The video offered no evidence that Musk’s $44 billion deal (£38bn) to acquire Twitter is complete.
Representatives for both Twitter and Musk have declined to comment on that, although a spokesperson for Twitter has confirmed the video is real.
A deadline of Friday to complete the deal was ordered by the Delaware Chancery Court in early October.
It marks the latest step in a rolling legal battle during which Musk signed a deal to acquire Twitter, then tried to back out of it, leading Twitter to sue the Tesla CEO to force him to conclude the deal.
If the two sides don’t meet the Friday deadline, the next step could be a November trial.
The entrepreneur was expected to visit Twitter this week and is expected to return again Friday if the deal is finalised, according to an internal memo reported by Bloomberg News.
The Washington Post reported last week that Musk told prospective investors that he plans to cut three quarters of Twitter’s 7,500 workers when he becomes owner of the company.
Several hours after posting his sink video, Musk tweeted that he was meeting “a lot of cool people at Twitter today,” but did not give further details.
Musk, 51, has shared few concrete details about his plans for the social media platform.
However, some technology analysts have speculated that Musk wants to use Twitter to help create an “everything app", similar to China’s WeChat service, which allows users to do video chats, message, stream video, scan barcodes and make payments.
