"We've monitored it very closely," Rodgers told Fox. "We've had representatives from Liverpool at most of the games.
"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.
"[His future is] nothing to discuss now. It's something we'll speak about at the end of the season."
The Hammers are thought to be open to keeping hold of Carroll, while his former club Newcastle United are reported to be considering a summer bid.