The 6ft 9in hitman maintained his unbeaten record - and kept himself on course for a major heavyweight fight - with a one-sided fifth-round stoppage win over Vinny Maddalone on Saturday to claim the WBO intercontinental title.
Earlier this year, Fury vacated his British and Commonwealth crowns - leading to accusations he was avoiding Price - but the 23-year-old insists he will fight this opponent when the time is right.
He told the Manchester Evening News: "I can see it happening, but it is another fight that I've got nothing to gain from. What will I gain from beating him? Nothing.
"If one of us won the world title, then it would be a good defence.
"I don't think it should be wasted on the British title. It deserves to be a big title fight.
"Let him build up his record and one day it will happen."
Fury is eyeing a period of dominance ahead of British fighters Price, Dereck Chisora - whom he has already beaten - and previous world heavyweight champ David Haye.
He added: "Whatever happens, I will have a new era of my own. I will rule the division.
"Price, Haye, Chisora - there is no outstanding British heavyweight. They are all beatable."
While Fury wants to fight one of the Klitschkos when he becomes the mandatory challenger for their world titles, he is keen to take on former IBF cruiserweight champion Tomasz Adamek.
He added: "I'm still undefeated. I would like to say I'm ready for anyone in the world. The Klitschkos? Bring them on. The Americans? Bring them on.
"Bring on Tomasz Adamek. He's too small for me and I see an early win for me."