The 20-year-old striker is widely regarded as one of English football’s brightest young talents, but he has been struggling to earn a regular spot in the first team at Manchester United under Jose Mourinho.
Rashford has been limited to just one start in the Premier League so far this season under Mourinho and he has only featured in three of the Red Devils opening four top flight games.
Romelu Lukaku is clearly ahead of the youngster in the pecking order at Manchester United and former Liverpool FC defender Carragher feels that Rashford could follow a similar trajectory as the Belgian did before he ended up at Old Trafford.
Speaking to Sky Sports after England’s win over Switzerland on Tuesday night, Carragher said: “Romelu Lukaku is in front of Rashford and I don’t see Rashford displacing him as long as he is there.
“But remember when Lukaku was at Chelsea and he had to come away and go to Everton. Then he ended up as top scorer and got his move to Manchester United.
“Possibly Everton is the sort of club you are looking at, just below the top six, for someone like Rashford, similar to what Lukaku did.
“You know you are going to play every week as the centre-forward and you know if you have a couple of games where you don’t score then you are still going to play the next week.
“Last season after they played Brighton away, Mourinho had a little pop at him and Lukaku went straight back into the team. That’s the problem you will always have.”
Manchester United will return to Premier League action on Saturday evening when they travel to Watford.
It has been something of a mixed start to the new campaign for Mourinho’s men, with the Red Devils having won two of their opening four Premier League games so far this term.
Manchester United have not won the title since back in 2013.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news