The Sun on Sunday claims that the Leicester stopper is seen as a ready-made replacement for the Spaniard, who has suffered a huge slump in form. Dean Henderson, meanwhile, is not yet considered to be ready for the role of No 1.
Schmeichel, son of Old Trafford legend Peter, still has three years left on his King Power deal.
But the 2016 title winner, 33, would be relatively cheap to buy - compared to Atletico Madrid's highly-rated Jan Oblak, who has a release clause of around £109million.
SunSport states that Red Devils boss Ole Gunnar Solskjaer has doubts over whether Henderson is ready for the top job. That is despite a stellar season on loan at Sheffield United.
And the Norwegian can no longer offer his blind support to error-prone De Gea.
Schmeichel has proved a consistent performer at Premier League level.