Rashford has been the most used player at United since Jose Mourinho took charge at the start of the 2016-17 season but has found game time limited after Alexis’ arrival from Arsenal at the start of the year.
Premier League rivals Arsenal and Tottenham Hotspur are reportedly Rashford’s keenest suitors but Parker, who made 105 appearances for United, believes he can’t leave.
Speaking to the Daily Star, he said: “I believe he has to stay if he’s got anything about him. He’s a local boy, he wants to prove a point. I wouldn’t say he’s had the opportunity that he would’ve liked but he has to stay.
“But then if he does stay then he’s going to have to maybe deal with the fact that he isn’t going to be able to play where he wants to play. I can see that he quite enjoyed being in the middle, he had a little bit of freedom. I don’t think he wants to be stuck on the touchline but he’s not going to get that at Manchester United.”
Rashford was one of the players who failed to impress in United 1-0 defeat at Brighton & Hove Albion on Friday night and now faces a fight in the final two Premier League games to get into contention for a place in the FA Cup Final squad.