The England international has been repeatedly linked with a move away from Anfield this summer, with Newcastle United and West Ham United both believed to be interested in the player.
However, Rodgers has insisted that Carroll could stay at the club beyond this summer after the 23-year-old played during the team's goalless draw with Tottenham Hotspur in Baltimore.
The Northern Irishman told the club's official website: "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."
Carroll moved to Anfield from Newcastle for £35m 18 months ago.