Media reports have claimed United are growing increasingly concerned over Greenwood's attitude in training and off the pitch.
And Townsend, who suffered similar scrutiny in his early career at Tottenham, says Greenwood must do everything he can to work through the situation.
Speaking on talkSPORT, the Crystal Palace winger said: "Of course it starts with the player himself, but I can empathise with Mason Greenwood having been through that "build you up to knock you down" media scrutiny.
"It's tough and he needs players around him like Harry Magiure, experienced players who have been through it, to put their arm around him. He needs his manager to stay by his side, which I know Ole probably will.
"He needs family and good friends around him, and the other thing is he needs to see a sports psychologist. Somebody who has spoken to other players in his position and who knows what's going on from the outside to help him through it.
"I have no doubt Mason Greenwood is a very young player who seems to have his head screwed on. Yes, he's made mistakes, but, yes, he is young and learning. If he gets over this little blip he's on then he will get to the other side a better player."