Old Trafford chief Erik ten Hag has a goalkeeping issue on his hands with Dean Henderson set to join Nottingham Forest on loan, Lee Grant having departed and Tom Heaton wanted by Middlesbrough.
Fifth-choice goalkeeper Nathan Bishop could be allowed to leave on loan to continue his development.
Manchester United have zeroed in on Ibrox custodian McCrorie as a potential addition and the goalkeeper would be willing to consider the move.
McCrorie managed just two appearances for Rangers over the course of the recent season and was keen for more game time.
He is entering the final year of his contract at Rangers and if Manchester United come calling then the Gers will have a decision to make.
If McCrorie does not sign a fresh deal then he could talk to interested clubs in January, ahead of a move next summer.
McCrorie, 24, has had loan stints away from Rangers, spending time at Livingston, Queen of the South, Berwick Rangers and Greenock Morton.
