Carroll's future has been the subject of intense speculation this summer, with the Hammers believed to have made a loan offer to Liverpool with a view to a £17m transfer.
Nolan played with Carroll at Newcastle United and says that the England striker would be a big hit at Upton Park.
He told The Mirror: "I would be delighted if Andy Carroll would come and join us here.
"I am not too sure whether Brendon Rogers will let him out but there is lots of speculation but there always is surrounding Andy.
"If there is a chance we would be in the reckoning with him because he is such a quality player."
Hammers manager Sam Allardyce has been vocal with his interest in signing Carroll and continues to pursue a deal for the 23-year-old striker.