The Tesla boss, who has a history of making irreverent tweets, tweeted on Wednesday: "I'm buying Manchester United ur welcome."
But when asked on Twitter if he was serious he replied: "No, this is a long-running joke on Twitter. I'm not buying any sports teams."
Musk's initial tweet would have caused a frisson of excitement amongst United fans.
Many have protested in recent years against the American Glazer family, who bought the club in 2005, due to the team's struggles on the pitch.
Manchester United have been champions of England a record 20 times and have won the European Cup, the most prestigious club competition in the global game, three times.
As of Tuesday's close, the football club had a market capitalization of $2.08 billion.