The Reds boss believes the 24-year-old has the potential to flourish in the Premier League, though it is not certain whether he will get the chance to do so at Anfield
Carroll joined Liverpool for £35 million in 2011 but struggled to make an impact and has since been loaned out to West Ham, where he has scored five goals in 17 appearances this season.
However, Rodgers has insisted that the 24-year-old can still flourish at a team that suits his style of play.
"Do I think he can be a top player? Is he a top player? He certainly has that potential,” Rodgers told reporters. "If he gets that opportunity of playing in a team that suits his style, then there's always a chance.
"It was very unfortunate for Andy when he joined this club because he had limited experience of the Premier League.
"Through no fault of his own he arrived on the back of an incredible price tag for someone so young and inexperienced, and the early stages were difficult for him.
"But there's no doubt Andy has great qualities. Look at one of his two goals last week for West Ham from the corner (in a 3-1 win over West Brom).
"There are not too many better sights in football when you've the big guy going and heading the ball like that.”
Regarding the target man’s future, Rodgers admitted that Liverpool’s stance on him is still unclear and that a decision could only be made at the end of the season.
"As to his future, there are other things involved, it's not as simple as him being here. There are other things we need to consider in it all," he added.
"As I've said, it's one where we will see it through to the end of the season and we'll take it from there."
Carroll is ineligible to play for West Ham against Liverpool in their Premier League encounter on Sunday.