The 27-year-old spent the second half of last season on loan at Aston Villa following a high-profile falling out with new manager Ruben Amorim.
Rashford was dropped for the crucial Premier League clash with Man City, to which he responded by telling journalist Henry Winter that he wants a “new challenge.”
United have since given his number ten shirt to new signing Matheus Cunha, signalling their intent to get rid of him as soon as possible this summer.
Per The Athletic, the England international has reported back to United training despite being granted permission to seek a move away from the club.
He will not be involved in team training, however, and will be forced to work on his fitness alone for the foreseeable future.
Antony, Alejandro Garnacho, Jadon Sancho, and Tyrell Malacia have all also asked to leave the club and are weighing up their options.