The IBF, WBA and WBO heavyweight champion had to watch on as WBC holder Wilder and Tyson Fury fought out a thrilling draw in Los Angeles a fortnight ago.
The WBC has since ordered a direct rematch, which if it goes ahead would leave Joshua on the edge of the biggest fights in his division.
But Joshua insists he wants part of the action.
“April 13, in London. I don’t know what more I have to do to get that message across. He’s (Wilder) more interested in fighting Tyson Fury – Tyson Fury holds no world titles.” Joshua told American show First Take.
“I can’t control what Deontay Wilder does, what Tyson Fury does, or what they say. What I can do is control what I do and say.
“I made sure with the negotiations I booked the date in advance, the venue in advance, and am making my point clear for everyone, I am willing to fight any one of these guys, especially the champion Deontay Wilder, at Wembley, April 13.”
Wilder this week said Joshua’s team was “begging” for a fight, while the Brit says he would much rather fight the American than domestic rival Fury.
Fury is the lineal heavyweight champion having surrendered the belts he took off Wladimir Klitschko in November 2015 when he took time out of the sport.
He remains undefeated since, but Joshua said: “I’m not interested in Tyson Fury, he’s not the champion.
“When I was joining the heavyweight ranks it was WBO, WBA, WBC, IBF… I don’t know where this lineal has popped out of the woodwork from.
“But if I’ve got to get my hands on that too, and that’s a belt that the world is interested in, Fury can step in if he’s serious.
“I want to fight the champion, I’m the one leading the pack, I’ve been doing that since I made my debut.
“Five years in, seven title defences and I’m running the game and I don’t know what more I have to do to get that message across.”