The 24-year-old looks almost certain to leave London Road this summer after rejecting the offer of a new three-year contract with the League One club.
Leeds boss Brian McDermott has expressed an interest in the midfielder but Fry insists the Championship side to not have sufficient funds.
He told the Peterborough Telegraph: "I've had Brian McDermott (Leeds manager) on the phone about Tommy and I've also spoken to their chairman Ken Bates and their chief executive Shaun Harvey, but Leeds just don't have enough money.
"We're sorry to be losing Tommy, but he's made it clear to us that we could offer him £20,000 per week and he still wouldn't sign a new deal.
"That's not to say he won't be here next season because we won't give him away. And if Tommy is here we know we will continue to get 100 per cent from him as he's a terrific lad."