Magpies boss Alan Pardew saw a bid to bring Carroll back to St James’ Park on a season-long loan rejected by the Reds last week and are now said to be mulling over a second offer.
The England international left St James’ Park 18-months ago to sign for the Merseyside club in a record £35 million deal but has failed to live up to that price tag.
Pardew is keen to be reunited with the 23-year-old on Tyneside as he prepares to lead his side into the Europa League but was knocked back with his initial proposal.
Rodgers has admitted he will listen to offers that would see Carroll leave Anfield permanently but says he isn’t prepared to let him depart on a temporary deal with Fulham and West Ham United also thought to interested.
“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.”