Rodgers loaned Carroll to West Ham United at the start of the season, and while refusing to reveal where he thinks the 24-year-old's future lies, the former Swansea City boss believes that the England international can have a significant impact for the remainder of his career.
The 40-year-old told reporters: "There's no doubt Andy has great qualities. Look at one of his two goals last week for West Ham from the corner. There are not too many better sights in football when you've the big guy going and heading the ball like that.
"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.
"But do I think he can be a top player? Is he a top player? He certainly has that potential. If he gets that opportunity of playing in a team that suits his style, then there's always a chance."
Carroll has scored five goals in 17 appearances for West Ham.