The 19-year-old has only made one appearance for the Red Devils this season, playing 68 minutes of their Champions League group-stage clash with Young Boys in December.
Amad has only made the bench for one Premier League match this season, meanwhile, and is not believed to be in Ralf Rangnick's plans for the second half of the campaign.
According to the Manchester Evening News, Man United are working to secure a loan exit for the Ivory Coast international before the end of the transfer window.
The report claims that the youngster would have left Old Trafford on loan last summer had he not suffered a training-ground injury.
Feyenoord, in addition to a number of Championship teams, are said to be interested in the attacker, with Man United keen for him to continue his development away from the club.