The England international has been linked with a move away from Merseyside after he struggled to make an impact since joining from Newcastle for £35million in January 2011.
But Rodgers is adamant the striker, who came off the substitutes' bench in Liverpool's pre-season goalless draw against Tottenham in America on Saturday, is still in his plans for next season.
Asked if there had been any offers for Carroll, Rodgers said: "Not that I am aware of. Obviously I'll know more when we get back.
"There has been a lot written about Andy, but you saw today he's happy to be here and he's worked very well since he's been here.
"The reality is he's still a Liverpool player, he can fit into how I want to play, and he's happy here.
"I'm certainly not wishing to push him out of the door."
Newcastle have had an initial offer to bring Carroll back to Tyneside turned down.