Carroll's future has been a hot topic throughout the summer, with West Ham United and former club Newcastle United reportedly interested in signing the player.
At one point it seemed as if Rodgers was keen to sell the England international, but he insists that he hasn't had a problem with the 23-year-old, and also claimed that Carroll had been left unfazed by the speculation.
"He's coped with the speculation fine. Unfortunately you cannot control what is written and the speculation out there, but he's coped well," said Rodgers.
"We've spoken, our communication has been open and he's worked very hard on the training ground since he has been here and since I have been here. I haven't had a problem with him.
"He knows where he stands within the group. We will see how that develops."
Liverpool get their season underway against West Bromwich Albion tomorrow.