Wilder will defend his WBC title against mandatory challenger Dominic Breazeale next month, with Joshua then set to make his American debut at Madison Square Garden on June 1 against an unnamed replacement for Jarrell Miller, expected to be Andy Ruiz Jr.
The unification bout against WBA, IBF and WBO champion Joshua appears no closer to coming to fruition.
However, Wilder recently insisted it was inevitable and Finkel anticipates it will finally happen next year.
"He's fighting his mandatory now, then we have a pretty full slate for this year, then we will discuss fighting Joshua next year," Finkel told Thaboxingvoice.
"The name calling, the immaturities that are in the press, they won't help but won't hinder making the fight.
"They are all in the works. There is nothing confirmed at this point, the only thing that is locked in is the fight with Breazeale on May 18.
"If everything goes the way we hope it will, we will then discuss his next fight.
"I have spoken with John Skipper [Executive chairman of DAZN, Joshua's American broadcast partner] more than once. Him and I are developing a very good relationship, I'm very fond of him.
"Those talks will continue, and eventually it will lead to a fight of Deontay and Joshua.
So many people are quick to cast stones at those who dare to be great.
Yet they have no idea what it takes to be a KING. #BombZquad #TilThisDay #Discipline #Sacrifice #PAIN #WilderBreazeale #May18th #PBConSHOWTIMEpic.twitter.com/A0tu7zSSuU
— Deontay Wilder (@BronzeBomber) April 27, 2019
"I think that on his [Wilder's] resume, the same as one Joshua's, it's a fight that should and will happen, and it's a fight that will be remembered because there was such a build up, very difficult to make.
"But the fight will happen and the fans will get to see it."
Wilder and Fury fought to a thrilling draw in December, and Finkel is hopeful a rematch can happen this year despite the Gypsy King having signed with ESPN and the American being contracted to Showtime.
"He's someone we continue to speak with as well," Finkel added.
"The difference is, in the negotiations with Fury, we're dealing directly and it's not in the press, there's no name calling, there's no gamesmanship.
"That fight will also happen when it's ready, which will be in 2019 I believe. If that fight is to happen, it would be a joint promotion."