Dan Rafael ESPN Senior Writer 7 Minute Read

Anthony Joshua hopes to fight Deontay WIlder for all the marbles sooner, rather than later. Mike Stobe/Getty Images

Unified heavyweight world titleholder Anthony Joshua came to New York this week to get the ball rolling on promoting his American debut against Brooklyn's Jarrell "Big Baby" Miller and they put on a spirited war or words.

There was even a little shoving mixed in at their kickoff news conference, but besides discussing his fight with Miller, which will take place on June 1 (DAZN) at Madison Square Garden, Joshua fielded numerous questions about the other two big names in the division who loom as his biggest, most lucrative opponents -- titleholder Deontay Wilder and lineal champion Tyson Fury.

They are the three legs of the so-called heavyweight stool, and while Joshua-Miller is viewed by most as a worthy fight between unbeaten big men, it is really showdowns with Wilder and Fury that garner the most debate and interest.

Although Joshua, who will be making his seventh title defense, said he is "not taking Miller lightly" and that he has "to buckle down" in order to prepare for him, Joshua also openly discussed his interest in fights with Wilder and Fury.

Wilder is on top of his list. It's a fight that has been discussed for the past year but has not yet happened. Each side blames the other.

Wilder (40-0-1, 39 KOs) hoped to fight Joshua (22-0, 21 KOs) this past fall, but when no deal could be struck, Joshua retained his three major belts by a destructive seventh-round knockout of mandatory challenger Alexander Povetkin on Sept. 22, and Wilder fought to a disputed draw with Fury on Dec. 1.

Joshua, a huge star in his native England, then hoped to make the fight with Wilder for April 13 at London's Wembley Stadium, where he has drawn sold-out crowds upwards of 90,000. When no deal could be made for him to fight Wilder or Fury (27-0-1, 19 KOs), his countryman, Joshua accepted the deal to face Miller (23-0-1, 20 KOs) and come to the United States to fight for the first time after previously not showing much interest.

"You could see in the U.K. the market was booming in boxing. There was no rush to go anywhere else," Joshua told ESPN in an interview on Thursday. "But there was (Matchroom Boxing promoter Eddie Hearn's) partnership with DAZN, and we knew we had to fight here one day. I didn't think it would be so soon.

"We booked the date [April 13] and the venue [Wembley Stadium] to get the undisputed championship of the world fight together [with Wilder] and that didn't happen. So I was like, 'Eddie, I need the next-best option.' He said, 'We're going to go to the States for a fight' and I was like, 'Perfect.' I liked the idea. It's a new challenge."

In December, Joshua (22-0, 21 KOs), 29, accompanied Hearn to New York, where he co-promoted Canelo Alvarez's fight with Rocky Fielding at Madison Square Garden. Joshua enjoyed his time in the big city, meeting with media and taking in the fight in front of an electric crowd. He said that experience made him more seriously consider fighting in America.

"I just want to come here and be involved in a culture and in replicating what we have in the U.K.," he said. "It's just the start of something new in my opinion. I can come to MSG and be a part of this American fanfare and get involved. You have the biggest media, the biggest outlets. To be here, with my feet firmly on the ground, kind of helps cement the reason why I'm here. It is very important for my own reputation to get involved in some of these big fight nights here."

While the fight with Miller is a big one indeed, it pales in comparison to what a fight for the undisputed world title with Wilder would mean or even one with Fury.

Miller shoves Joshua during staredown Jarrell Miller comes face-to-face with Anthony Joshua and gives him a hard shove during their staredown at Madison Square Garden.

Joshua said he would be happy to fight Fury but very much wants Wilder in order to secure the fourth belt he needs to earn recognition as the undisputed heavyweight world champion.

"I've got three now. I'm not interested in stopping," Joshua said. "Wilder is just another hurdle in my way. I have no interest in stopping before I get the last one. It's something that has to happen and that's why I spoke to Eddie, and I said I think we need to start a conversation [well before the Miller fight was signed] because these fights take a long time to get a signature on the bottom line, and we can't wait.

"I'm going for all of [the belts]. I'm not going to stop at this one now when I've come so far. Forget the money, who would I rather fight, Wilder or Fury? I'd rather fight Wilder because it's an opportunity to fight for the belt."

Joshua said he wasn't sure if Wilder had the same desire because of the fact that once he had the draw with Fury -- and before the WBC ordered a rematch -- Wilder and his team did not show any serious interest in making the undisputed fight for the spring.

"He had the opportunity for April 13," Joshua said. "He had already fought Tyson Fury. He had a draw and now he has the opportunity to fight whoever he wants. He chose to fight Tyson Fury [again]. There's a question you have to ask him -- why isn't this fight with me happening? Because of that fight in December, it's a blessing because it was a close fight and he got a draw, which meant he kept his hands on the belt. But now when it's a situation where he has to make a calculated decision and ask himself what he really wants to do, because he has an opportunity to choose legacy over having an easy touch, and he chose to fight Fury as an easy touch when he could have fought for legacy and history April 13 for the undisputed championship of the world."

The prospect of the Wilder-Fury rematch happening, at least next in the late spring or early summer, became more unlikely earlier this week when Fury pulled a surprise by signing a co-promotional deal with Top Rank to fight exclusively on ESPN platforms.

Joshua viewed Fury's decision to align with Top Rank and ESPN as good for the prospects of a Joshua-Wilder fight.

"I think it made mine and Wilder prospects easier," Joshua said. "I don't know why Tyson Fury [signed with Top Rank] while in negotiations [for the Wilder rematch], but he did what's best for him. I feel like it just shows Wilder that now he's not the relevant party. He's not the one bringing the money to the table. DAZN and ESPN are. Showtime (where Wilder has been aligned) aren't bringing anything to the table, so Wilder's not in control, and he needs to kind of humble himself and get on board before it's too late and me and Tyson Fury end up fighting."

Joshua said that of course it would be easier to make the series of fights between him, Wilder and Fury if they were all aligned with the same broadcaster. But he said he was hopeful they could still be made. Wilder claims he has no network contract even though Showtime has invested heavily in him. Joshua hopes that means a quicker path to fighting Wilder.

"I think Wilder, if he misses another opportunity, he could be left out for a little while," Joshua said. "He might have to fight someone like [Miller, who] I have to fight in the meantime who's a danger man for him and he might get beat in the process.

"That's what I'm going through now, so I need to get past Miller so I can put my sites on fighting [Wilder], and he needs to fight and win so he can put his sites on fighting me before this year is out. The longer we leave it the less likely the fight will happen."