Price extended his unbeaten record over the weekend with a first round knockout of John McDermott, a fighter Fury struggled against over the course of two bouts.
The Liverpool fighter is now the mandatory challenger to Fury's British title and the Price camp want to arrange a showdown between the two unbeaten prospects.
But Price thinks that while Fury may want to test himself against the Olympic bronze medallist, he may view the fight as too much of a risk from a business standpoint.
"He'll want the fight, I want the fight, but boxing is a business," Price told Sky Sports News.
"It doesn't make business sense for him to fight me now because he'll lose his undefeated record and any potential bigger fights down the line."
Price's promoter, Frank Maloney, indicated that there will be no hesitancy to negotiate from his side of the table as he openly called out Fury, who is also the commonwealth champion.
Maloney said: "Fury - we've challenged you. We want your belts, we want your world ranking rating. So please make sure you turn up."
Maloney also believes that Price will eventually surpass the career earning of his former client Lennox Lewis, but the 28-year-old boxer remained a little more circumspect.
"At this stage, I'd bite your hand off to achieve a fraction of what Lennox Lewis achieved," Price said.