Currently on-loan with Getafe, the forward's form has brought Greenwood to the attention of clubs across Europe.
Barcelona, Atletico Madrid and Juventus have all expressed interest.
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The Sun says Greenwood appears to have accepted he won't be returning to Old Trafford, having made his home available for rent.
A source said: The fact it's on the market is a strong indication Mason has no plans to return to United.
The house was his home when he hit the big time with the club.
It was also where he was ordered out of bed by detectives when he was arrested, and became his sanctuary when waiting to find out if he was going to be charged."
Greenwood has rebuilt his career in Spain after assault charges in January 2022 were dropped.