Having reclaimed the IBF, WBA and WBO world titles with victory over Andy Ruiz Jr in Saudi Arabia, Joshua is eager for a unification bout with the undefeated WBC champion Wilder.
Wilder must first however get past Tyson Fury with the two set to meet in their hugely anticipated rematch on 22 February.
Joshua meanwhile has his own mandatory title defences to make before he can realistically challenge for the WBC belt with Kubrat Pulev and Oleksandr Usyk in place for shots at the IBF and WBO straps respectively.
But the Briton believes he and must Wilder must deliver what he believes will be a legacy fight for both men.
“Wilder is a talented fighter but he’s just another fighter to me that I’d like to challenge,” Joshua told JD Sport’s In The Duffle Bag podcast.
“I promise you, before he’s done and before I’m done... we’re in the same era, the same division - heavyweights, both got some belts and it would be crazy for the history of boxing a thousand years from now when none of us are here... oh they never fought?
“So for politics or none, but for legacy and history this fight will definitely happen.”
Anthony Joshua was speaking to JD as part of their ‘In The Duffle Bag’ podcast series. Download from iTunes, Spotify and A-cast and leave a review for the chance to win 2 x tickets to AJ’s next fight. www.jdsports.co.uk