Carroll linked up with the Hammers on a season-long loan at the start of the 2012/13 campaign after being deemed surplus to requirements at Liverpool.
The England international has endured injury troubles at Upton Park, but has shown in glimpses what he is capable of when fully fit and firing on all cylinders.
Nolan feels West Ham could help Carroll to rediscover his very best form, but appreciates that he may feel as though he still has a point to prove at Anfield.
"Everyone at West Ham has really enjoyed working with Andy - and we all believe there is no better place for him to be than at our club," said Nolan.
"He's in one of the best cities in the world, playing with lads who want to play with him.
"He was probably a bit harshly treated by Liverpool and I think he feels hard done by with all that's happened there.
"I think most Liverpool fans were shocked by what happened to him in pre-season, after the way he came into his own with some of his performances towards the end of last season. But he still loves Liverpool and he has the hunger to prove to everyone there that he is good enough to play there.
"No one has spoken about what happens when his loan spell with us is up but everyone in our dressing-room will want Andy to stay beyond the end of this season.
"Only time will tell where Andy plays next season. We feel we're a good fit at West Ham but he's only scored two goals for us so far so he's going to have to get his finger out or we won't want to buy him."
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