Fury, the WBC heavyweight champion, turned professional in December 2008, nearly five years before Olympic champion Joshua, who holds the WBA, IBF and WBO titles in boxing's blue riband division.
"Fury has been professional much longer than me. He should be looking to retire soon," Joshua told Sky Sports. "If he wants to cement his legacy, I'm here and ready. I've built myself into this position.
"I came up quick. That shows I'm ready. These boys (Fury and Wilder) turned professional in 2008 and it took (Fury) seven years to fight for the heavyweight championship of the world. He's on a completely different journey.
"I want to steam through. I've fought five champions and been in two unification fights. I'm a two-time heavyweight champion in the space of 24 fights and a (seven-year) career. It shows you I am serious."
Fury, 32, became a world champion in his 25th fight when he dethroned the long-reigning Wladimir Klitschko in a performance for the ages in 2015.
Joshua clinched world honours the following year in his 16th contest when he stopped Charles Martin and the 31-year-old Watford fighter has since beaten Klitschko, Joseph Parker, Alexander Povetkin and avenged a defeat to Andy Ruiz Jr before beating Kubrat Pulev.
While a meeting with Fury – or even Wilder – would be widely regarded as blockbuster events, Joshua added: "These guys aren't the biggest names that I've fought on my record anyway. They are just another heavyweight.
"Look at my record. They are not the best fighters that I have challenged. I'll challenge Fury, I'll challenge Wilder. When they are ready, I'm here to fight.
"I haven't got fear of Fury – whether he's got a better chin than me, a better jab than me, whether he's all of this stuff that people say. So be it. Let me go in there and prove myself, show you who I am and what I can do."