The Reds have agreed a fee with West Ham for Carroll after the striker enjoyed a successful spell on loan at Upton Park this season.
Any move could be delayed after Carroll picked up a heel injury which could sideline him for up to six weeks, but Rodgers does not expect any possible move to drag on after the loan move only took place at the back end of the summer transfer window.
Rodgers revealed he has spoken to Carroll about his future and the Liverpool boss expects a resolution soon.
"It was just a general conversation in terms of the experience of getting out and playing," Rodgers told the Guardian. "He enjoyed that apart from the injury.
"At the start of the season the whole thing was about going and getting games because he wasn't going to be a starter here. We will talk again with him and the club to see how it all evolves. It's one of those situations where it will probably be resolved a lot quicker than that for both parties."
Rodgers admits he plans further talks with Carroll during the summer to try and thrash out the player's future.
"It's a difficult one. I spoke to him and we had a good chat," added Rodgers
"In terms of the money, that's something out of my control. But he's a talent so we will assess the whole situation.
"The objective at the beginning of the season was for him to go out and play. He's gone away to think of what we spoke about and we will talk again through the weeks."