The England striker has scored just two goals in 12 Premier League appearances for the Hammers after moving from Anfield to Upton Park.
The 24-year-old, who was signed by the Reds in a £35m deal in January 2011, has been forced to contend with a series of niggling injuries since joining West Ham.
But Nolan says Carroll is determined to do well in the second half of the season to prove that he still has what it takes to be a success at Liverpool.
“He loves Liverpool,” Nolan told the Mirror.
“He still wants to prove to everybody he is good enough to play there. He has that hunger – that’s what people don’t see.
“Andy was probably a bit harshly treated at Liverpool. I think most Liverpool fans were shocked at him getting loaned out.
“You have to take it on the chin. He’s big enough and ugly enough to do that and get on with him. I think he’s done that.”
Carroll and Nolan have been close friends since their time together at Newcastle United, and the Hammers skipper is enjoying having the target man around Upton Park.
However, the former Bolton Wanderers midfielder admitted Carroll needs to start scoring more goals if the forward harbours any ambitions of sealing a permanent switch, should his Liverpool career come to a premature end.
“I think Andy’s perfect for us and we’re perfect for him,” he added.
“Sam is 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.
“But he’s got to score goals or we won’t buy him, will we? He’s only scored two. He’s got to start pulling the finger out for us if he wants us to buy him!”