The Sun claim there is concern about a major squad overhaul and Ryan Giggs' position should the former Chelsea boss replace Louis van Gaal.
Mourinho is on the brink of an agreement with the Red Devils and has even told close friends he will be in the Old Trafford dugout next season.
After losing the dressing room at Stamford Bridge just a few months after winning the Premier League title, there is a fear the cycle could repeat itself at United.
Juan Mata will be one player particularly worried as Mourinho sold him when he was at Chelsea.
Despite many feeling the Portuguese manager taking over to United is a done deal there are also reports that the Red Devils have made contact with Mauricio Pochettino.
The reports say Sir Alex Ferguson is a fan of the Tottenham boss and his emphasis on giving young players a chance.
United supremo Ed Woodward is keen to stick with Van Gaal and ideally wants him to see out the final year of his contract.
With United dumped out of the Champions League in the group stage, and sitting outside of the qualifying places for next season's competition, a change is looking more and more likely.
The Dutchman takes his side to the Stadium of Light to face Sunderland on Saturday in the Premier League.