Fury recently withdrew from negotiations for a clash with the British champion for a second time, leading some to claim the undefeated traveller doesn't fancy the bout.
But Liverpudlian Price believes his undefeated nemesis would, in fact, face him at the drop of a hat and is eager to "strike while the iron's hot" and make the fight as soon as possible.
The world title hopeful told Press Association Sport: "Do you know what - I don't believe Fury would back out of a fight with me.
"But I do believe the people around him are viewing it as a dangerous prospect.
"Fury's not clever enough to think 'I'll wait and do this and that first'. He'd just run in and fight me tomorrow, I know that for a fact.
"It's the people around him. They've got the brains and they are thinking 'David Price is a big puncher and a dangerous opponent, this could all end very quickly.
"I think it's down to them. They want to wait until there's more money in the fight and that's fair enough. I don't blame them."
It could be argued that the huge all-British fight would be worth more further down the line, when one or both men have a world title.
But 29-year-old Price, who takes on well-regarded American Tony Thompson on Saturday, is not so sure it is worth risking.
"It does make more sense to wait but there's no guarantee of it happening, that's the thing," he said.
"As I've said with heavyweight boxing, so much can change so quickly. One punch can change everything.
"Sometimes it's about striking while the iron's hot and I think in six months, this fight is going to be as big as it's ever going to be without a world title on the line.
"How long's it going to take for one of us to get a world title? Who knows, because of the politics of the sport?"
Price (15-0, 13KO wins) added: "Fury isn't in a position to fight for the WBC title yet because there are three people in front of him and there's other politics, for example David Haye might come into the equation (to fight WBC champion Vitali Klitschko).
"There are a lot of things in the way of Fury fighting for a world title anytime soon and in the meantime I think we may as well just get it settled, fight each other and then crack on."
Price aims to prove his world title credentials when he makes a step up in class against respected veteran Thompson at Liverpool's Echo Arena this weekend.