Rashford was one of several United players to struggle this season, scoring just five goals in 37 appearances in all competitions.
The 24-year-old surpassed 300 appearances for his boyhood club last month but his future at Old Trafford is more uncertain than ever.
Rashford was considering a move away from United earlier in the year after being repeatedly overlooked by interim manager Ralf Rangnick, but is said to want to revive his United career under Ten Hag.
However, that decision could be taken out of his hands and Anfield hero Carragher is of the opinion that Rashford is ‘not good enough’ for Manchester United and is instead at the level of ‘Arsenal or Tottenham’.
‘He’s just not quite good enough for Manchester United, Marcus Rashford,’ Carragher said on Sky Bet’s The Overlap show.
‘That’s all it is. That’s it, he’s not quite good enough for Manchester United. He’s Tottenham or Arsenal.’
United legend Gary Neville was also on the show and disagreed with his Sky Sports colleague, saying: ‘He’s proven he’s good enough. I can’t let you get away with that.’
But Carragher responded: ‘He’s not going to win you the league or the Champions League. You’d need the two up front with him to be megastars and he’d be the addition.’
Neville then said: ‘That’s like saying Divock Origi is not good enough for Liverpool, or Xherdan Shaqiri isn’t good enough for Liverpool.’
Carragher ended the debate with: ‘OK he’d be a squad player. He’s not good enough to be in the first XI to win Manchester United the big trophies, he’s just a level below that.’
Earlier in the show, Neville had backed Rashford to improve under former Ajax boss Ten Hag and explained why he thinks the England international has been struggling.
‘I think Ten Hag will look at Rashford and think he’s a project I can work with,’ Neville said. ‘I think Ten Hag will look at him and think he’s quick, he runs, if I can give him some coaching I think I can work with him.
‘I think with Rashford for me it’s a combination of the disease that’s been in United’s dressing room this season, confidence of every single player, the scrutiny including ourselves on television.
‘There’s no doubt that the mass campaigns that he’s had off the pitch which to be fair have achieved more than he’s achieved on the football pitch must take it’s toll, with people contacting you all the time from a non-football perspective.
‘He’s there and paid to be a Manchester United football player and he’s got almost like a second job which to be fair is giving him far greater reward in terms of what he’s achieving.
‘He’s achieving unbelievable things but that is a massive pressure that on a kid. To live up to on and off the pitch the expectation of being that man Marcus Rashford.
‘You’re kneeling down in front of the Queen one minute and then the next being asked to play football.’
Manchester United finished sixth in the Premier League this season – 13 points behind fourth-placed Spurs and 35 points adrift of champions Man City.
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