The versatile Rowe has turned down Peterborough's offer of a new three-year contract, prompting Leeds manager Brian McDermott to enquire about the 24-year-old.
But Fry told the Peterborough Telegraph: "I've had Brian McDermott 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. If Tommy is here we know we will continue to get 100 per cent from him as he's a terrific lad."
Leeds signed 6ft 6in striker Matt Smith from Oldham earlier this week and are reportedly close to completing a deal to take Reading forward Noel Hunt to Elland Road.