Rodgers insists there is 'absolutely no way' he would allow the former Newcastle No 9 to leave on loan, but accepts the Reds will consider any offers they receive.
Only last week Rodgers said the £35million England international does not figure in his plans and "he can go out on loan".
Newcastle have already seen one loan approach turned down and West Ham boss Sam Allardyce admitted their own talks of a loan deal came to nothing.
Rodgers: "There has been a lot of unfair criticism of Andy, there has been a lot of speculation in the press in terms of not being able to fit into my style of play. I think that's unfair.
"If a club spends £35m on a player, you would expect that player to be able to fit into whatever style a manager will bring in.
"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.
"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.
"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.
"We are a top club, that doesn't change. Liverpool is still synonymous around the world; it is a club that has great history.
"Players will want that challenge to come and play for Liverpool and see if they can get the club into that position.
"I don't think the attraction of playing for Liverpool has deteriorated, but players want to play at the highest level and it's our job as a football club to try and challenge and to get players here that want to accept that challenge and can arrive back at that level."