Carroll is currently on loan at West Ham United after Rodgers allowed him to leave Anfield following his debut season with the Reds. The England striker, signed by Kenny Dalglish for £35m in January 2011, is waiting to discover if he has any future with the Reds following several reports that Rodgers is willing to sell him.
Rodgers is believed to want around £17m for Carroll but when asked about the player on Thursday, he was keen to play his cards close to his chest.
"It's nothing to discuss now. It's something we'll speak about at the end of the season," Rodgers told Fox Sports. Carroll, 24, has scored five goals in 17 appearances during his injury-hit spell with the Hammers, including a double in last weekend's win over West Bromwich Albion.
Rodgers has kept an eye on Carroll's form and he hopes the former Newcastle United star can make a strong finish to the season. "We've monitored it very closely. We've had representatives from Liverpool at most of the games," Rodgers added.
"It's obviously been a difficult season for Andy because his initial idea was he wanted to go out and play every week, but unfortunately for him he's picked up some injuries since he's been away. But he scored two very good goals at the weekend and he'll be looking to finish the season on a high and achieve the objectives he wanted to before he went out."