Joshua will take on the Ukrainian on Saturday night with 90,000 people expected to travel to Wembley Stadium.
The Brit will defend his IBF title, with the vacant Super WBA crown also up for grabs this weekend.
Wilder is planning to be ringside for the fight and he has urged his rival to win so they can meet in the near future.
"I would love to scrap with both of them but particularly Joshua," he exclusively told Sky Sports.
"Now, even though he is fighting Klitschko, the fans - even over here - want a Wilder-Joshua fight. For me, over here in the US, it is a bit strange they are all talking about and advertising us [Wilder and Joshua] and asking people who they want to see.
"Everyone wants to see it and I am all for giving the fans what they want.
"You only see mega-fights in boxing once in a while and in the heavyweight division, I think that would be the most exciting and the best in the history of heavyweight boxing for a long time."