The two Brits are set to finally meet this summer with Joshua, holder of the IBF, WBO, WBA and IBO titles, and Fury, the WBC champion, putting their belts on the line.
Saudi Arabia is set to host with 14 August all but certain to be the date.
It promises to be an enthralling fight between two of the best of their generation.
But Haye, a world champion himself in his career, believes Joshua has what it takes to stop the unbeaten Fury.
"I like the dedication of Joshua and I think he has a good chance of winning it early," he said.
"People think I’m crazy but that’s just the way I see it. I loved his fight against Wladimir Klitschko - he took his licks and got back up and showed the heart of a champion."
Haye believes Fury's style doesn't match up well against Joshua and predicts he'll run into trouble early.
"Tyson isn’t so much of a one-punch specialist," he added. "He puts his punches together and his style is that if you throw big looping shots at him he’ll make you look silly.
“But AJ throws hard, compact punches and he puts them together well. I don’t see this fight going smoothly for Fury at all."