Both Price, the British and Commonwealth Heavyweight Champion, and Fury earned wins at the weekend over Matt Skelton and Kevin Johnson respectively.
But the pair appear no closer to facing each other in the ring as Frank Maloney, who acts for Price, and Fury's promoter Mick Hennessy continue to clash over the terms of any deal.
However Price, 29, believes agreement can be reached and said: "It's going to happen - it's got to happen," he told Ringside.
"Everyone deserves the fight to happen, not least me and Tyson Fury so hopefully we can get something sorted and get the fight made.
"There are a lot of political issues - things getting said back and forth. If the fight is going to get made, hopefully somebody can get in touch and then, obviously, I believe I'll be the better man on the night."
Price - who needed only one minute and 22 seconds to knockout Audley Harrison in mid-October - put in another dominant performance last Friday as he extended his unbeaten run to 15 professional fights with a quick-fire victory over Matt Skelton.
Despite stopping his opponent with two minutes and 56 seconds gone in the second round, Price admitted his performance was more functional than flair-filled.
"It was a satisfactory result for me," he reflected. "It was a difficult fight for me to get up for. I had a massive win against Audley Harrison and literally couldn't enjoy it because I was in the gym a week later to prepare for this fight because it was pretty soon after.
"So I was a little bit tired mentally in the build-up but I got the job done. Matt's a marauding, come-forward fighter.
"He makes things difficult, he makes things ugly and he's a bit rough with the head. I wanted to get him out of there before any injuries came in and I blasted him out in the end.
"I'm not disappointed in the performance but it wasn't as good as I probably could have performed - and I'm probably my worst critic - but simply because if I had someone more dangerous and better in front of me I would have raised my game.
"He surprised me at first because he jumped on me straight away and I wasn't expecting it. I thought he might feel it out a little bit but he just literally ran across the ring at me.
"When I hit his head I realised it was a hard head and I was going to end up hurting my hands so I thought I'll go downstairs and see if he can take it downstairs and luckily for me he couldn't."
In contrast Fury's clash with Johnson in Belfast was slow-paced and went the distance before the Briton won unaminously on points 119-110 119-108 119-108.
The win improved Fury's unbeaten record to 20 fights and puts him in line for a possible shot at Vitali Klitschko if WBC heavyweight champion decides to return to the ring, but Price was unconvinced by the manner of his victory.
"It was pretty controlled," he said. "He showed improvements technically but Kevin Johnson came in with a sparring partner's mentality. You could go all night at the pace that the fight was fought at.
"But still, Fury got the job done. Johnson got in and just survived really - that's how he fights. I'd have tried a bit harder to get the job done earlier but if I'd realised that I couldn't get him out of there, then I would have stuck to my boxing. But I think I would be able to get Kevin Johnson out of there."