The England striker has been linked with a loan move to AC Milan in recent days amid suggestions he will struggle to adapt to Rodgers' preferred playing style.
Asked about Milan's interest Rodgers denied any contact, but the new Reds boss stopped short of giving Carroll a ringing endorsement.
Rodgers told Sky Sports News HD: "I haven't heard anything from them at all.
"He's a good player, Andy. He'll always be linked to clubs whether he's here or not. I spoke to Andy on his holidays, and he knows where he stands."
Asked again whether Carroll is a part of his plans, Rodgers said: "Initially it's about assessing the squad, you never know until you come in. The pre-season is broken up due to the European Championship.
"But certainly come the start of the season I hope to have the squad that I can take through. It's a case of building a squad that can compete at the top of the table."
Rodgers has also hinted that he is prepared to offer a clean slate to Joe Cole and Alberto Aquilani, two players that have been sent out on loan in recent seasons after struggling to settle at Anfield.
Rodgers added: "Both players are back. I had a good chat with Alberto the other day. He's a good guy and it obviously hasn't quite worked out for him as of yet. But he's a player that has got the qualities, the technical ability, to play.
"What's going to be important for every player is that they have the steel and the mindset to play. That's something I will find out about all of the players during pre-season."
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Support the USA national team with an official 2013 Centennial soccer jersey from Nike. Its Official.