The forward is currently on the sidelines, with injury ruling him out of the Hammers strong start to the season.
Impressive displays from Diafra Sakho, Stewart Downing and Alex Song have risen the club into the top 10, with a number of first-team stars still on the road to recovery, and the Europa League could be a real possibility if the club continue to perform in the same manner.
But Carroll is aiming bigger than the Europa League, with European football’s greatest competition the real aim.
With the club set to move into the Olympic Stadium in 2016, the increased revenue could see the club fighting for Champions league qualification, and the former Liverpool and Newcastle man is confident the Hammers can take advantage of the move - with everything falling into place for the club.
He told the Evening Standard: “When I first signed for the club the manager [Sam Allardyce] said this team could get into the top six and into Europe, and I can see the plan coming together now — it is not out of the question.
“With the players we have I can’t see any reason why we can’t do that. We could definitely play in the Champions League in the new stadium. The quality is there, and with the new stadium coming we have everything else going for us.”
Carroll has yet to experience the Champions League in his career, although he played one season in the Europa League with Liverpool, as well having a cameo role in Newcastle’s UEFA Cup campaign in the 2006/07 season.
The Magpies were said to be interested in securing the services of their former youth prospect, but with the future looking bright for the Hammers, he has no reason to leave the Boleyn Ground, and he has a desire to see out his future with the East London club.
“It looks fantastic and everyone is looking forward to being there,” he added. “We cannot wait to be a part of it.”
“It’s going to be one of the best grounds around — both the inside and outside look fantastic.
“We went in there when we first got it and it was empty, and it still looked great. I can only imagine what it will be like when it is full with all the fans.”