The British duo have been trading insults, which culminated in Fury calling out Price after the latter's knockout victory over Audley Harrison on Saturday night.
The 29-year-old also claimed that Fury should seek medical help for his attack on the Liverpudlian, and Maloney claims that a fight between the two could sell out Anfield.
"We're happy to sit down and start negotiating and get this fight on. I read in the papers he says this fight is personal and he wants [to fight] Pricey. Well, there is nothing stopping this fight being made apart from him and his promoter," Maloney told talkSPORT.
"Tyson Fury has got a very big mouth. He uses Twitter as a way of getting out messages but real men fight they don't just make noise. We will make this fight at the drop of a hat.
"[It would happen] sometime in the new year. It's a big fight that needs time to put together. It's a big fight that would sell out Anfield. We are willing to sit down and talk. We are opening the door to Mick Hennessey and Tyson Fury to come forward and start talking."
Price is the current British and Commonwealth heavyweight champion.