The Anfield club are understood to have turned down a bid from the England international's former club Newcastle to re-sign him on a season-long loan earlier this month.
Carroll's Liverpool future is still far from certain, though, after a disappointing first 18 months on Merseyside since his £35 million move from the Magpies.
Rodgers told Sky Sports News: "I've spoken openly and honestly with Andy in terms of where he is at, but I have done the same with all of the players, I have spoken to all of them, I have had communication with all of the group.
"It gets highlighted more with Andy because he is a young player. Maybe others may not see him fitting in with me, but for me he is an important part of the group.
"There is talk of him going on loan, but there is absolutely no way I would be looking to loan a player like that, especially after the investment the club have paid. But his condition will be the same as every player. If an offer comes in for any player at the club we would either look at it, or dismiss it, and Andy's no different to that."