The unified world champion will defend his WBA, WBO, and IBF heavyweight belts against 'Big Baby' Miller at Madison Square Garden in New York on June 1.
Joshua, 29, frustrated fans when he announced he would make his US debut after failing to agree a Wembley fight against either Deontay Wilder, Tyson Fury or Dillian Whyte.
AJ is the heavy favourite against the Brooklyn Brawler, who has racked up 23 wins out of 24 fights, with 20 victories coming by way of knockout.
Despite this, Miller has drawn parallels between his fight with Joshua and Buster Douglas' shocking 1990 upset of Mike Tyson at the Tokyo Dome.
He said: “I think it will be between the same lines, but you look at all the Brit’s over the years that did well but as soon as they come to America they get smashed.
“Whether that’s Prince Naseem, Amir Khan the tale goes back, there’s a lot of Brit’s that come on American soil and get smashed.
“They do great at home, but when they come over to America it’s a different story. He’s made a big mistake.
“His team are in unfamiliar territory, he’s got to step out his comfort zone and do certain things and protein shakes won’t help.
“I’ve been the underdog before and proved myself many times. AJ thinks he’s going to come over and run over me? Never happened, and never will."
Khan, who hasn't fought since his devastating knockout loss in Las Vegas to Saul 'Canelo' Alvarez in May 2016, admitted later that the fight was a mistake.
Before that, a complacent Prince Naseem, was considered the best 126lb boxer in the world before he was humbled in a 12-round clinic to Marco Antonio Barrera.
Promoter Eddie Hearn had reportedly offered Dillian Whyte a £4million payout to face Joshua at Wembley as a 'Plan B' after failing to land both Wilder and Fury.
Miller added: “I thought the Dillian Whyte fight was what he really wanted, but AJ was trying to be cheap and they didn’t want to pay Dillian Whyte the offer he wanted.
“AJ has a funny way of negotiating when he’s losing, he tries to put in contacts where he rules over the rematch.
“So when I knockout AJ on my rematch he wants to have the majority and Whyte didn’t want that.
“If I’m the champ and I beat you, I call the shots – what happens on the undercard, negotiations – but AJ didn’t want that, so that’s why the Dillian Whyte fight fell through.
“On my part, I have a good network in DAZN, and Matchroom and Eddie Hearn wanted to make the fight.
“It was never about the money, but the same time the money was there and I know what I’m gonna bring to AJ to get the rematch going.
“It was spoken about for about a month and a half but I just wasn’t super excited about it – I’ll be real.
“But the paperwork came through about a week and a half ago, and I was like ‘Okay, this might be happening’.
“AJ was like ‘I’m not doing this, I’m not doing that’ but DAZN said they could agree it.
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