Wilder extended his record to 39 wins after a stunning KO of Bermane Stiverne in Brooklyn last night.
The American was in explosive form, getting the victory in the first round with a deadly left-right combination.
The victory ensured his sixth successful defence of his WBC heavyweight title.
Many are calling for the Wilder to face Joshua, who beat Carlos Takam last weekend in Cardiff to retain his IBF and WBA belts.
And after beating Stiverne, Wilder sent a defiant message to Joshua.
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“I want Joshua. Joshua come and see me baby,” Wilder told Sky Sports.
“No more diving, no more ducking, no more dodging. No more excuses.
“Let’s make the fight happen. Let’s see who is the best. Are you up for the test?
“My belt says the heavyweight champion of the world.
“I will go anywhere in the world. Anywhere in the world. I’ll go to England as well.
“Make a date. Let it happen!”
Joshua meanwhile, admitted last weekend he wasn’t ready to spread his wings yet and fight in the bright lights of Las Vegas.
He said: “I want to continue growing the sport of boxing.
“It’s not my decision what happens out the ring, but what do you want UK?
“We’ve got London, Wales, Ireland and Scotland.
“Where else? Vegas? I think people want me to stay here.
“It’s a beautiful thing – look at what boxing is doing.”