The 51-year-old Tesla and SpaceX CEO, who has a habit of posting provocative statements on social media for fun, said: "Also, I’m buying Manchester United ur welcome," in a reply to an earlier tweet about supporting both of America's two major political parties.
Manchester United, a storied English football club, is currently led by the six children of late American businessman Malcolm Glazer, who took a controlling stake in the franchise in 2005.
Shares of the team listed on the New York Stock Exchange are down year to date, but ended Tuesday flat, with a market capitalization of $2.1 billion.
The Glazer family also owns the Tampa Bay Buccaneers, an NFL franchise in Florida.
There was no immediate reaction from the club or its owners to Musk's tweet.
Manchester United fans have protested the team's management for poor performance in recent years, as well as their involvement in a plan to start a new "Super League" of Europe's richest teams.
The Red Devils finished last season at sixth place in the English Premier League, but have gotten off to a rocky start this year.
After two straight losses, including a humiliating 0-4 defeat last weekend at Brentford, Manchester United currently sit at dead last -- the first time they have been at the bottom of the chart in 30 years.
More protests against the Glazer family's ownership of the club are planned ahead of United's next game at home to Liverpool on August 22.
As for Elon Musk, the richest man in the world recently sold nearly $7 billion worth of Tesla shares, and is in a major legal battle in the US state of Delaware over his aborted plan to buy Twitter.