The Daily Mail says the billionaire will swerve the Old Trafford game with protests against him and fellow owners, the Glazer family, planned by supporter groups.
United currently sit in 16th place on the Premier League table and defeat by Villa could see them drop to 17th - one place above the relegation zone.
Earlier this month, a statement from supporters group The 1958 read: "Our final home game of the season is against Aston Villa. We march, as one fanbase, to make it clear - 20 years on, the fire still burns red, with fury and defiance. We protest, once again, at Villa.
"May 2005 marked one of the darkest days in the history of Manchester United Football Club. The Glazer family became majority shareholders, triggering a compulsory takeover that was completed on 29th June 2005.
"That moment signalled the beginning of the end for the soul and community of our once-great club - sacrificed at the altar of corporate greed. Sir Alex Ferguson, a staunch supporter of the Glazers then and now, masked the damage with unprecedented success on the pitch."
Rot laid bare
"Since his retirement, the rot beneath has been laid bare for all to see - the true cost of 20 years of financial exploitation and mismanagement. The club is drowning in over a billion pounds of debt. Our fanbase is fractured and divided, our stadium neglected - down to Glazer greed and betrayal.
"Hundreds of millions have been siphoned off to service that debt - not by the Glazers, but by our club. All while the Glazers continue to pocket dividends, year after year, regardless of failure on the pitch. Old Trafford, once the Theatre of Dreams, is crumbling from decades of neglect. They've taken everything.
"Now, even Sir Jim Ratcliffe's arrival has come at the cost of hundreds of jobs, further punishing a fanbase already suffering under the Glazers' reign. Lifelong, loyal supporters are being driven away from the club they love - priced out and pushed aside.
"Another dagger in the heart of our footballing community. We want the Glazers out of our club. They were never welcome. They are not welcome now. They will never be welcome."