Rodgers has held discussions with Carroll about what the future holds following a successful season at West Ham United.
"I spoke to him and we had a good chat," said Rodgers. "The boy is a talent. It' s just something we need to assess between now and the end of window. 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. It was just a general conversation in terms of the experience of getting out and playing.
"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."