The war of words between the two camps has rumbled on and last week, Fury's promoter Mick Hennessy claimed comments made by Maloney were the only stumbling block to the fight being made.
British and Commonwealth champion Price, 29, has halted his last nine opponents and will follow November's demolition of Matt Skelton by fighting former world title challenger Tony Thompson in February.
Fury, meanwhile - still just 24 - fought a higher-profile opponent in Kevin Johnson and claimed a unanimous decision over the American in front of a raucous Belfast crowd.
A clash between the two Britons has been touted for some time now and as the British Boxing Board of Commission have ordered it, Maloney insists the Fury camp is simply looking for excuses and running scared of the Liverpudlian giant.
He told the Sky Sports Toe2Toe podcast: "Will the fight happen? It should do for the public. We're willing to sit down and negotiate. If Mick Hennessy wants me to apologise for my remarks about Tyson Fury and that'll help make the fight, then I apologise."
Maloney went so far as to compare Hennessy's behaviour to that of Rock Newman, who prevented his fighter Riddick Bowe from facing Lennox Lewis in the heavyweight showdown the world was waiting for in 1993.
Maloney added: "If you don't want to fight, be honest. Dealing with Mick Hennessy is like a reincarnation of Rock Newman and Riddick Bowe. They don't want the fight and I don't blame because they'd get beaten and they wouldn't the chance to fight for a world title.
"Maybe David will let him fight for his world title once he becomes champion.
"David Price will be fighting February 2rd against Tony Thompson at the Echo Arena in Liverpool. That'll be going up and on sale some time next week.
"It's a great fight. Price is well established in America. His last two fights will be shown on TV over there and this will be too. Price has caught the public's imagination.
"People said his career was going nowhere but I believe we have an art in developing heavyweights. He's the most successful Olympian from 2008."