Joshua climbed off the canvas to eventually stop the legendary Ukrainian in the 11th round and earn the biggest win of his young career and extend his record to an unblemished 19-0.
The victory cements Joshua as the leading heavyweight in the world and leaves him with his pick of opponents with big names seemingly lining up to take him on.
Klitschko has already hinted at a possible rematch while WBC champ Deontay Wilder has said he would relish a unification bout with an all-British clash with former world champion Tyson Fury is perhaps the most box office option of all.
And Joshua admits that he would like his next fight to capture the imagination of the public, whoever it may be against.
The Brit, whose fight against Klitschko was a played out amidst a backdrop of mutual respect, said: "At the end of the fight they (the British fans) cheered Wladimir but, yes it would be nice to fight a real villain.
"We can definitely find someone to dance with again, to bring that sort of attention again. Anyone with a belt is good, to add more to the (collection). We could rematch Klitschko again.
"I think that would be good because of the type of fight we had. And I think even guys without a belt would be good. Tyson Fury obviously hasn't got a belt.
"(Fury represents) a fight that would bring massive attention from the top to the bottom."
Fury has not fought beating Klitschko in November 2015 and last year he surrendered the titles he won in that fight to focus on his mental health problems.
It remains to be seen when, or if, Fury returns to the ring but both he and Joshua have been actively urging the other to make a potential showdown between the two undefeated heavyweights become a reality.
A rematch with 41-year-old Klitschko is also a possibility for Joshua and would prove a similarly lucrative and high-profile option to facing Fury.
When discussing a potential return with Joshua, Klitschko - whose points defeat by Fury in 2015 means he has lost twice in succession - insisted he had a rematch clause he could choose to exercise.
Klitschko inflicted a first knockdown of Joshua's career with a devastating right hand in the sixth round of Saturday's clash, but in the 11th the Ukrainian suffered his second and third knockdowns of the fight before being stopped on his feet - potentially reducing his desire for a rematch.
Joshua said: "I think he will want to (fight me again) because a fighter is the last one to know when it's time to stop. But I think the team around him, ie his wife, and they normally wear the trousers, and his brother (Vitali), they will advise him differently."
Additional reporting by PA