Miller and Joshua have clashed previously at the DAZN announcement back in July in the US.
The 30-year-old New Yorker called AJ a "punk" to his face and promised to "whoop him".
Unsurprisingly this evoked an angry response from Joshua who told Miller he would "slap him".
"Big Baby" Miller is desperate for a step into the big time and challenge for heavyweight world titles.
But first he must get past unbeaten Romanian Bogdan Dinu on November 17.
Speaking ahead of a fight many expect to be over early, Miller, who has 22 wins with 19 KOs, said: "I want those big names, the Anthony Joshuas, the Dillian Whytes, Deontay aka Beyonce Wilder – you know I can’t stand that guy.
"So, let’s get this win and then if Dillian doesn’t fight AJ, I can turn that English muffin into toasted strudel!”
Undoubtedly Joshua is the fight most heavyweights want, not least because he holds the WBA, WBA, IBF and IBO world titles.
And the fight most boxing fans want to see isn't Miller against Joshua, but Wilder against the Brit for all the titles.
But WBC king Wilder has blasted "coward" Joshua after receiving "the worst offer in boxing history" for a potentiqal unification scrap.
The Bronze Bomber, 33, now claims he's moved on to the "biggest fight in the world" as he prepares for his upcoming clash with Tyson Fury.
Wilder added he believes British star AJ is scared of him as he prepares for his next fight in Los Angeles on December 1.
The American said: “He was just a coward, straight out. He was just a coward and he didn’t want to fight.
"When a guy allows his people to not accept $50million dollars (£39million), that’s a guarantee, you don’t want to fight.
“When a guy offers me a $15m flat fee, which is the worst offer in boxing history for a fight of this magnitude, they still didn’t want it.
“With that being said, they don’t want to fight. They just want to trick people, manipulate them, contradict and just be compulsive."
Wilder went on to say he's ready for bigger and better things, adding: “We’ve moved on and now I’m in the biggest fight in the world, with Tyson Fury.
“[Joshua] needs someone to narrate the conversation, a middleman. I’m a grown man, I don’t deal with boys.
"I don’t need another man to reply to someone else, when we are right here face-timing each other.
“I think he’s a little fearful of me, so we’re gonna let him be."
Wilder defends his WBC belt against Fury at the Staples Center in Los Angeles on December 1.
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