The former Newcastle United and England star believes Three Lions captain Rooney's desire to represent his country at another major tournament could see his club form with the Red Devils suffer.
Shearer was critical of the midfield role Rooney played in England's 1-0 win over Slovakia in World Cup qualifying on Sunday and suggests that Tottenham Hotspur youngster Dele Alli could be played in his place, in turn affecting the 30-year-old's positioning at United.
"Dele played the role that Rooney should have been playing last night.
"But even if Rooney starts deeper, he needs to be further up the pitch than he was last night in general play.
"I said last week that maybe it is time for Rooney to give up on international football for his own good, to concentrate on his club career.
"He wants one more crack at a major tournament and good on him for that. But I fear he will suffer for it at a time when there is huge competition for places at Old Trafford."