Wilder will attempt to defend his WBC heavyweight title against Dominic Breazeale on Saturday night.
The American had been in negotiations with Joshua over unifying the division for well over a year before talks broke down.
But those negotiations could be picked up if Wilder beats Breazeale and Joshua gets the better of Andy Ruiz on June 1.
Wilder’s long-term trainer Deas believes the pressure is now so high that it is inevitable that the pair must go toe-to-toe.
“It depends if the powers that be can come together,” Deas told Sky Sports.
“We offered AJ $50million and they said no. They then offered up £15m and we said yes.
“I don’t have any doubt as to who wanted the fight and who didn’t.
“The pressure is so much that, when these guys come through these fights, there will be a renewed charge to make it happen.
“You’ve also got Tyson Fury saying: ‘I’m also in the mix, I’ve got a draw with Wilder, I want that again’.
“It is going to get real interesting.”
Joshua is in his own training camp ahead of his bout with Ruiz but he is still planning to tune in and watch Wilder this weekend.
“Styles make fights, I think Wilder will fare well against Breazeale,” Joshua said.
“I think Wilder is too quick, he’s a very, very fast heavyweight, but Breazeale is tough, took me seven rounds.
“I hope Wilder does it in nine, so I can be like ‘hey I done it earlier’.
“You know how it is, comparisons and stuff, but yeah it will be interesting to see.
“You look at the small things, I look at the small details – when he’s getting tired, how many right hands he throws in a round. I look at something different, rather than comparisons to the rounds.”
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