Musk, the world's richest person, had said on Twitter that he wanted to buy England's most successful soccer club before clarifying later - much to the dismay of United fans - that it was a joke and that he had no interest in purchasing any sports teams.
The club's owners, the American Glazer family, are under pressure with United sitting bottom of the Premier League after two games of the season.
Bloomberg reported they would consider selling a minority stake, opening the door for Ratcliffe.
"If the club is for sale, Jim is definitely a potential buyer," Ratcliffe's spokesperson told the Times on Wednesday.
"If something like this was possible, we would be interested in talking with a view to long-term ownership."
The Glazers have been the target of intense criticism for their failure to invest in the team who have not won a trophy in five years.
United's net debt had grown 11% to about Stg 496 million ($A864 million) by the end of March.
The owners have also been criticised for not improving the Old Trafford stadium, the biggest club ground in the country with a capacity of around 75,000 fans.
Ratcliffe, head of chemical company INEOS, is from the Manchester area and a long-standing fan of the club.
"This is not about the money that has been spent or not spent. Jim is looking at what can be done now and, knowing how important the club is to the city, it feels like the time is right for a reset," the spokesperson added.
Ratcliffe failed this year in an attempt to buy London club Chelsea which was ultimately bought by an investment group led by Todd Boehly and Clearlake Capital.
United finished sixth last season in their worst Premier League campaign with respect to points earned, failing to qualify for the lucrative European Champions League.
The club hired manager Erik ten Hag from Ajax Amsterdam in a bid to turn around their fortunes but the Dutchman has not yet succeeded in imposing his playing style, with United losing their opening two games after conceding six goals.
United play their arch-rivals Liverpool, who scored nine times without reply in their two league meetings last season, at Old Trafford on Monday.
