The Red Devils are yet to determine whether or not the 21-year-old forward will be absorbed back into their first-team squad.
He has been pictured training with a private instructor, but those sessions are taking place away from Carrington.
Greenwood was suspended by United in the wake of physical and sexual abuse allegations being made against the ex-England international.
Those charges were dropped in February 2023, but an internal investigation at Old Trafford remains ongoing.
The Telegraph reports that a final ruling on Greenwood will be made in the wake of a “strategic review” regardless of how takeover talks progress in Manchester.
United are still waiting to discover who will be calling shots from the boardroom heading forward, with the Glazer family delaying a process that has seen interest expressed by Sir Jim Ratcliffe and Sheikh Jassim bin Hamad Al Thani.
The Premier League outfit need to know how much money will be made available for reinforcements in the summer transfer window, allowing them to identify which positions are prioritised.
Greenwood will not impact those plans when it comes to players that can operate in the final third of the field, with a decision on his future set to be made soon.
The forward has not figured for United since January 2022, but he remains under contract on full pay and was included on the club’s retained list at the end of the 2022-23 campaign.