According to La Repubblica, the Turin club have made a serious enquiry about the player's status, following a similar request from fellow Serie A club Atlanta.
Greenwood has not played for United since January 2022 after being charged with attempted rape, coercion and assault. Those charges were dropped in February of this year, leading Man Utd to open their own internal investigation which is still ongoing.
The player remains suspended and unable to take part in pre-season training, although has been spotted training individually and pictured keeping fit alongside United team-mate Anthony Elanga.
United got their friendly programme underway against Leeds United on Oslo on Wednesday, while the club's board continue to evaluate what to do about Greenwood in terms of reintegrating him or cutting him loose.