Fury has claimed that he would end the 32-year-old's career should they meet in the ring, and Booth believes that the potential bout is the most "natural heavyweight fight" available.
Booth told The Sun: "David against Fury is the most natural heavyweight fight out there. It is the most logical high-profile fight in Great Britain, if not the world, right now.
"Both boxers are great entertainers. Fury is doing a great job inside and outside the ring and David is a former two-weight world champion.
"I am waiting to make contact with Fury's promoter to see if the interest expressed in some of his comments are genuine or just hot air from a young fighter."
Haye is scheduled to name the opponent for his comeback fight within the next week, while Fury stopped American Steve Cunningham inside seven rounds last weekend.