Rashford burst onto the scene last season, with the 18-year-old emerging from the youth ranks to earn a place in the first XI and an unexpected trip to Euro 2016.
But Allardyce has expressed his fears that new United manager Jose Mourinho will turn to experience rather than youth under the pressure of a Premier League campaign.
“Jose’s job is to win the title, but I hope Rashford plays,” said Allardyce. “It will be down to the lad himself. He’s a talent, and if Jose sees that talent emerge like it did last year, then the boy picks himself.”
Rashford’s rise might have come at a dizzying pace but he is happy to slow things down again as he looks to establish himself in the Old Trafford set-up.
“I’m preparing for the new season now,” he said. “There’s no need to rush into anything. I’m taking my time, taking it steady.”