The family has held some preliminary discussions about the possibility of bringing in a new investor, but are not yet ready to cede control of the English soccer club, which could be valued at about 5 billion pounds, according to the report.
Manchester United did not immediately respond to a Reuters request for comment.
Earlier, Elon Musk said in a tweet that he was going to buy the club – only to say a little later it was all part of “a long-running joke”.
Manchester United was bought by the American Glazer family for 790 million pounds ($954.48 million) in 2005. Although it has been listed on the New York Stock Exchange since 2012, the Glazers retain majority ownership.
United fans have been clamoring for a change of ownership at the club – the three-time winners of the European Cup, the most prestigious club competition in the global game – following its disappointing performance in recent years.