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.
His former club have, however, already had an initial offer to bring Carroll back to Tyneside turned down.
But Rodgers is adamant the striker, who came off the substitutes' bench in Liverpool's pre-season goalless draw against Tottenham in Baltimore on Saturday evening, 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."
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!