The 20-year-old is rated as one of England’s brightest prospects in the Premier League, despite Rice previously committing to the Republic of Ireland before changing his allegiance.
The former Chelsea FC youth star has established himself as a key part of Manuel Pellegrini’s team over the past 12 months thanks to his imposing performances in the middle of the park.
Rice was linked with a potential move to Manchester United in the summer as Ole Gunnar Solskjaer looked to improve his Red Devils team with the addition of young English talent.
However a transfer failed to materialise amid talk of West Ham placing a £90m price tag on the youngster to warn off potential suitors such as Manchester United.
Quizzed about whether Man United should consider a swoop to sign Rice, former Liverpool FC defender Carragher told Sky Sports:
“Would I pay £90m for a holding midfield player? No I wouldn’t. But do I think Declan Rice is of the quality where eventually he’s going – whether in 18 months or 12 months – to play for a Champions League team, I think he can.
“There’s no doubt he still has to improve, yes he can get better in terms of his angles, receiving the ball off the back four.
“If I was a top four team, and I was in Manchester United’s position and looking for a midfielder, I’d have Declan Rice as that holding midfield player.
“Obviously the price, I wouldn’t pay £90m for him, of course I wouldn’t. But if you’re talking £50m, maybe more, I think he could do a job for a Champions League team.”
Solskjaer started his summer spending with the £17m addition of Welsh winger Daniel James from Swansea City.
The Red Devils boss landed Crystal Palace defender Aaron Wan-Bissaka in a £50m deal to bolster his back four.
Manchester United completed their summer spending with the £80m addition of Harry Maguire.
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