The Red Devils have made a mixed start to the new campaign under Ole Gunnar Solskjaer, with his side only managing to pick up five points from their first four games.
That run of results has left them seven points behind leaders Liverpool FC after just four games, and they are without a win since their opening weekend victory over Chelsea FC last month.
Manchester United are aiming to try and break back into the top four this season after they finished in sixth place and without a trophy last term.
However, former Manchester United goalkeeper Carroll has admitted that he is not sure whether the Red Devils have what it takes to seal Champions League qualification.
Speaking in an interview with TheSportsman.com, Carroll said: “It’s going to be difficult for Ole, but I hope they make the top four.
“I think they’ll make the top six, but I hope they make the top four for the Champions League. I think they’ll definitely make the top six.”
He continued: “I was with Ole when I was a player here and his mindset is that he’s Manchester United through and through and he will change things here, which I hope he does, because he’s a really good guy as well.
“There’s a lot of former players who have surprised me that they’ve gone into manager, but Ole who was a substitute a lot, watched the game and came on and scored a lot of goals.
“However I didn’t see him as a future manager back in those days, just because at the time you’re not looking out to find out who will be the next manager you know? We just concentrated on how good he was as a player.”
Manchester United will return to Premier League action after the international break when they take on Leicester City in front of their home fans at Old Trafford on Saturday afternoon.
The Red Devils have not won the Premier League title since their famous final triumph under Sir Alex Ferguson in 2013.
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