Rooney has been dominating the headlines for all the wrong reasons in the past week following his foul outburst in the win at West Ham.
The England star was charged by the Football Association for the incident and he has been ordered to serve a two-game ban after failing to appeal the length of the suspension.
It means Rooney will miss Saturday's Premier League clash with Fulham as well as next weekend's FA Cup semi-final against local rivals Manchester City.
There has been much speculation about Rooney's demeanour on the pitch and Schemeichel has come to the conclusion that a change of scenery could help the player.
"I think it would be good for him to get away," Schmechel told Ekstra Bladet.
"It would be good for him to play for another club. Real Madrid under Mourinho, is someone that could handle him and get the best out of him.
"It is painful to say that that the best player you have, which he is at United, he is better off trying something new.
"United will probably not sell him to another English club, but a change of scenery would help."