Garner scored 19 goals for the Cumbrians last term after joining the club from Blackburn, but chief executive David Allen has revealed that, under the terms of the youngster's contract, Rovers would receive £500,000 from any transfer.
Bristol City had a £1m bid for Garner turned down in January while Nottingham Forest have been linked with the player this summer.
But if any club ups their offer to £1.14m they will be allowed to talk to the player under a clause in his contract.
Allen told the News & Star: "We've always wanted to keep Joe. He's extremely popular with our fans and everyone at the club.
"Of course, he's also a great young player with tremendous potential who's working extremely hard to recover from a very serious injury, which is likely to sideline him for several more months.
"But there's nothing we can do to stop Nottingham Forest, or any other club for that matter, speaking to Joe once they've reached the £1.14m trigger.
"We've always wanted to keep Joe as a Carlisle United player and we're mindful that he still has two years to run on his contract with us."