The 22-year-old's current deal is set to expire and chairman Paul Baker admits their latest offer is unlikely to be good enough to keep him at the club.
"We've made him another offer and it's a decent contract, but I suspect it still won't be enough to compete with the other clubs coming in for him," he told the Gloucestershire Echo.
"However, it shows how much we value him and we've done all we can to try to keep him. I don't expect him to be here next season, but if he is it would be fantastic.
"If not, we will negotiate the best fee we possibly can which will go back into the playing budget."
Cheltenham would be entitled to a fee for Pack, who was very close to a move to Swindon in January, because he is under the age of 24.