The 21-year-old is currently on loan at Championship side Doncaster Rovers.
The Daily Mail says three clean sheets in his last five games has attracted interest from Burnley and Derby who are both eyeing him for next season.
David Moyes made it clear he has no intention of letting Johnstone leave United permanently when he handed the player a new three-and-a-half year contract in January.
But with David de Gea well-established as United's first-team goalkeeper, a host of clubs are ready to take Johnstone on loan next season.
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