Anthony Joshua and Deontay Wilder will experience a "renewed charge" to agree a fight, according to the latter's trainer Jay Deas.
Wilder defends his WBC heavyweight title against Dominic Breazeale at 2am on Sunday morning, live on Sky Sports, before Joshua defends the IBF, WBA and WBO belts against Andy Ruiz on June 1, live on Sky Sports Box Office.
Remaining unbeaten in their latest defences for what would become a combined 65th fight will increase excitement for an undisputed world heavyweight title fight between the two champions.
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"The pressure is so much that, when these guys come through these fights, there will be a renewed charge to make it happen," said Deas, Wilder's long-time trainer and manager.
"It depends if the powers that be can come together.
"You've also got Tyson Fury saying: 'I'm also in the mix, I've got a draw with Wilder, I want that again'."
Joshua will make his US debut at New York's Madison Square Garden a fortnight after Wilder's upcoming fight.
Asked if he would first keep an eye on Wilder, Joshua told Sky Sports: "Yeah, yeah 100 per cent."
Breazeale's only defeat in 21 fights came when he challenged for Joshua's world title in 2016. He was stopped in seven rounds.
But Joshua was impressed, and remembered: "When I looked at his interview after and I saw his face, I said 'wow you definitely took a beating', and he stayed in there.
"He got hurt in the second round, stumbled, stayed on his feet."
Giving Breazeale advice to fight Wilder, Joshua said: "Come game, it's a world championship fight, that's what I'm saying."
Breazeale has since rebounded from losing to Joshua with three stoppage wins in a row, and insists beating Wilder could cause the current champion to walk away from boxing.
"I think he finds it humbling and I think it ends his career, it retires him," Breazeale told Sky Sports.
Wilder's sparring partner Malik Scott added: "Breazeale is very tough, he's a big man, he's imposing. Deontay's plate is full but I believe he will pass this test with flying colours."
Watch Deontay Wilder's WBC heavyweight title fight against Dominic Breazeale at the Barclays Center in Brooklyn, from 2am on Sunday May 19, live on Sky Sports Action and Sky Sports Main Event.