Aged 20, Rashford has already made 150 appearances for Old Trafford club, as well as earning 31 England caps.
Former Everton boss Allardyce believes that the lack of time off he will be afforded and prospective injury problems that will mount up could prevent the youngster from playing for more than another decade.
“(It will) probably be very difficult to get to 30,” he told talkSPORT. “Because of the demand, physically and mentally he will suffer.
“He will have three weeks a year off. That's it. He'll play all over the world because there's no pre-season any more, they go playing straight away into these tournaments. He'll play for his country in the summer and he'll get barely three weeks off.
"When you look at the wear and tear that is by 25, he will have niggles, even if he doesn't have any major injuries. The knees, the ankles, the hips, the back will start being a little bit of a problem as he goes on.
"It won't stop him playing, but later on in life it would bring his career to an end quicker than maybe before."
Famously, Lionel Messi (31), Cristiano Ronaldo (33) and Luka Modric (33) all struggled once they reached the age of 30. Wait...
