Rashford, 20, is widely considered as the most promising talents to emerge from the United's academy in recent years, but Shearer is fearful he may never live up to his true potential as a centre-forward.
After bursting onto the scene as an 18-year-old under former manager Louis van Gaal, with four goals in his first two starts, the England forward has been restricted to a wing role since then.
A return of 32 goals in 126 games since his bow in the 2015/16 season has displayed his potential at the highest level and after scoring in the 2-1 defeat to Spain as a central partner to Harry Kane - Shearer explained why he may need to leave Old Trafford.
"As long as Romelu Lukaku stays fit he is not going to get a starting spot as the lone striker at Old Trafford," he told The Sun. "As long as Jose Mourinho is the manager, there is not going to be two up top.
"Even if Lukaku did not play, my money would be on Alexis Sanchez being moved into the middle and further forward.
"And would Mourinho really turn to Rashford if he needed another striker? Or would he go to the transfer market for a tried and trusted ready-made goalscorer?"
With four goals in 24 caps for the senior national team before the age of 21, time remains on the side of the Red Devils starlet - but Shearer went on to explain how playing in a different role can affect the progression of a natural finisher.
"Rashford has been played so long in a wide position in a three, that it does take time to readjust to his natural position," the former England captain said.
"Time is not a great commodity in football nowadays. I am not advocating Rashford moves away from Old Trafford.
"It is a great club to be at. But if he wants to achieve an ambition to be recognised as a great goalscorer it is just not going to happen there."