Joshua fought twice in 2017, beating Wladimir Klitschko and Carlos Takam to end the year 20 fights unbeaten as a professional and as the WBA and IBF world heavyweight champion.
Boxers around the world are queuing up for the chance to take on the Brit and his promoter Eddie Hearn has already outlined a plan to unify the division by fighting Joseph Parker and Deontay Wilder.
And while Nelson admits the Parker deal now looks all but done, the former cruiserweight world champion believes a clash with Haye would be an epic, if left-field, encounter.
“But then it comes to the last of the three and everyone will say Fury or Wilder, but I am going to go for David Haye,” Nelson told Sky Sports.
“Yes, that means I see him winning his rematch with [Tony] Bellew, but after that, him going in against Joshua will be a massive fans’ favourite.
“That, in late summer, what a fight that would be!
“Haye brings huge support with him, so does ‘AJ’, and everyone would have an opinion on that one.”
As Nelson mentions, Haye will first have to avenge his 11th round TKO defeat to Bellew from March.
Anthony Joshua stopped Carlos Takam on his last outing (GETTY)
The pair were due to get in the ring together for a second time on December 17, only for Haye to pull out with a bicep injury suffered in a freak training accident.
The fight has been rebooked for May 5, which will likely be just a few weeks after Joshua’s next defence.
And assuming Joshua makes it through Haye, Nelson is eying a third fight for the former Olympic champion in 2018.
“Joseph Parker is a given for the first one and then I am expecting ‘AJ’ to win it, but that’s when the fun starts,” Nelson added.
“Chuck in the mandatory then I guess I will have to go for Alexander Povetkin next – although I wouldn’t mind if Kubrat Pulev got his chance again.”