The Englishman has scored only two goals so far this Premier League season, during which a string of injuries has forced him onto the sidelines.
Despite Nolan wanting him to stay at West Ham, the skipper has revealed he wants to prove Liverpool were wrong to send him out on loan.
“He loves Liverpool,” Nolan told The Mirror. “He still wants to prove to everybody that he is good enough to play there. He has got that hunger - that is what people don’t see.
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“Andy was probably a bit harshly treated at Liverpool. I think most Liverpool fans were quite shocked at what happened to him in pre-season and him getting loaned out, but that’s football.
“You just have to take it on the chin. He’s big enough and ugly enough to do that and get on with it. I think he’s done that.”
Even though Carroll has kept his cards close to his chest regarding his future at West Ham, Nolan would love to welcome the striker to the club on a permanent deal.
“I think Andy’s perfect for us and we’re perfect for him,” said Nolan. “Sam [Allardyce, West Ham manager] is definitely the right man to get the best out of him.
“He’s in London, one of the best cities in the world. He’s playing for a great club, he’s playing with lads who know him, want to play with him. Only time will tell.
"You’ll never know what’s going to happen in the next window. We’ll just have to wait and see. But he’s got to score goals or we won’t want to buy him, will we? He’s only scored two for us.
“He’s got to start pulling his finger out for us if he wants us to buy him!”