Haye, who is recovering from an injured Achilles sustained in March's defeat to Tony Bellew, is still targeting a fight with Joshua and told Sky Sports: "I will find a way to beat that giant, he is 10 years younger, three inches taller and three stone bigger and I love and relish that kind of challenge."
Joshua will next defend his IBF and WBA 'super' heavyweight titles against Kubrat Pulev at Cardiff's Principality Stadium on October 28, and is not taking Haye's threat seriously.
"People are more relevant for calling people out than for actually fighting," Joshua says.
"If we fight, you'll hear all sorts from me about Haye. For now, I wish him a speedy recovery.
"It would be great if him and Bellew fight again. Once he gets that out of the way, if it happens, then he can focus on other players in the heavyweight division.
"Haye isn't in my top three [potential opponents]. My mandatory is Pulev, then Luis Ortiz, then I can start looking out to see what other options I have."
Joshua had previously revealed that he regards upcoming challenger Pulev and WBC champion Deontay Wilder as his two "biggest threats".
Asked about facing Wilder, Joshua said: "It's being talked about in America and in the UK. "Wilder is 38-0 with 37 knockouts, he's been pro for nine years since 2008 so experience is the best teacher. He's had loads of that.
"As I move forwards with my career, I'm learning. Every week, every month, every year that this fight gets put on the backburner, I'm maturing as a fighter.
"It will happen, it's just a matter of when.
"I don't know if we need to go to Vegas. It's a fight that demands a lot of seats, and the UK has a lot of space."