The striker spent last season on loan at Upton Park, with the Hammers subsequently having a £15 million offer accepted but the player is reportedly hesitant to join permanently
The striker spent the 2012-13 season on loan at Upton Park after being told first-team opportunities would be limited at Anfield and, after initially struggling for form and fitness, notched seven goals in 24 appearances.
Carroll - who joined Liverpool in 2011 for £35 million - is now the subject of an accepted £15m offer from West Ham following end-of-season talks with Rodgers, but is thought to be reluctant to join the mid-table outfit on a full-time basis.
|10/1||Liverpool are 13/8 with William Hill to finish in the top four next season
"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."
Goal exclusively revealed in April that Carroll is keen to prove his worth at Liverpool, but Rodgers admits he may well again find opportunities limited following the January arrival of Daniel Sturridge.
"It's a difficult one. I spoke to him and we had a good chat. 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."