Joshua, who holds the IBF, IBO and WBA (Super) Heavyweight Titles, was asked by Sky News who he thought his next opponent would be.
“We’ve got David Feathers (Haye) and Beyonce (Deontay) Wilder,” he replied before laughing, saying: “I had to do it”.
The words come just days after WBC Heavyweight Champion Wilder posted a video online criticising the British fighter for not fighting him.
Wilder, 31, appeared to goad Joshua in the video, describing him as not being physically, mentally or emotionally ready for the challenge.
Speaking to Sky News, Joshua said: “All these guys talk about me all the time and it’s negative, always negative, but sooner or later I’ll be ramming my jab down their throat.
“It’s not a matter of if, it’s just a matter of when when it comes to the likes of David Haye and Deontay Wilder because there has been no era of boxing where heavyweights, middleweights, welterweights haven’t come together.
“We have to fight each other and that’s just the way it’s going to go.”
Wilder was part of the 90,000 crowd that watched Joshua’s win over Wladimir Klitschko at Wembley in April, but he says that wasn’t enough for ‘AJ’ to make his name in the US.
On Sunday, he told Sky Sports: “To be global, you’ve got to make your name in America and Joshua is not as big as people think he is over here.
“The UK is about the size of Texas. One state in my country, where people don’t know who Joshua is for real.
“If my name was brought up and Joshua came along it’s the same as if Joshua’s name came up, my name would come along.
“It will be a great fight, but he is not that popular over here. I had to burst a lot of people’s bubble but he’s not.
“If he wants to be global, he needs to come to America to fight me, but to be honest, I don’t care where it happens.”