The Telegraph says Fletcher has been in talks over return to United.
Fletcher, 35, is out of contract at Stoke this summer and is expected to hang up his boots.
The Scot's last appearance came off the bench against Derby a month ago and he hasn't even made the bench in recent weeks.
He could return to United to work within a new recruitment structure at Old Trafford.
The Red Devils are set to bring in a sporting director this summer, with Fletcher possibly working alongside Mike Phelan.