The team is controlled by America’s Glazer family, which did not immediately respond to a request for comment.
The football club had a market capitalization of $2.08 billion at the close on Tuesday.
Manchester United fans have protested in recent years at the Glazers, who bought the club for £790m ($955.51m) in 2005, over the team’s struggles on the pitch.
The anti-glazer movement gained momentum last year after United were embroiled in a failed attempt to set up a breakaway European Super League.
Some fans have urged Musk to buy Manchester United instead of buying Twitter. Musk is trying to end a $44 billion deal to buy the social media company, which has landed him in court.
On Saturday, Manchester United suffered a humiliating defeat at Brentford, conceding all four goals of the game in the first 35 minutes.
The week before United had lost their Premier League season opener 2-1 to Brighton & Hove Albion. This was the first time since 1960 that the team had conceded at least six goals in the first two games of a top-flight season.
This is also the first time United have lost their opening two games since 1992, when the team won the title.