Carroll is a loan target for Milan.
He told Sky Sports News HD: "He's a good player, Andy. He will always be linked whether he was here or not.
"I have spoken to Andy on his holidays and he knows exactly where he stands. He's a very good young player and he will be linked with clubs like that because he's such a good player."
Asked if Milan had made an approach, Rodgers added: "I haven't heard anything from them at all."