Anthony Joshua Calls Out Deontay Wilder, Fight Me Already!

Anthony Joshua is turning up the heat on Deontay Wilder -- telling TMZ Sports he wants a crack at the Bronze Bomber ASAP ... and inviting the boxing superstar to "come see me."

Joshua and Wilder have been trading verbal jabs for years but have never been able to come to terms on a fight contract. A Joshua vs. Wilder matchup could be one of the biggest fights in PPV history.

Anthony invited us onto his tricked out sprinter van in NYC moments ago ... and walked us through his fight plans -- including some tough talk for Deontay.

Long story short ... Joshua says he wants to unify the heavyweight titles -- and since Wilder is the reigning WBC heavyweight champ, he wants to fight Deontay as soon as possible to get that belt.

"If he's ready and wants to prove he's the best in the world, [Wilder] can come see me," Joshua says.

Wilder is slated to fight Dominic Breazeale on May 18 -- and if he gets through D.B., he's got options ... including a rematch with Tyson Fury.

As for Joshua, he'll be fighting 29-year-old Andy Ruiz on June 1 -- after his original opponent, Jarrell "Big Baby" Miller, tested positive for a bunch of banned substances.

But, Joshua says he ain't holding a grudge -- he hopes Miller can turn his life around and get right.

In the meantime, Joshua says he ain't taking Ruiz lightly -- despite the fact most people don't know who he is.