A unification between Wilder and Joshua would push the mandatories back.
Joshua insists any fight with Wilder would not need to happen in America.
According to Punch, Finkel said he would be prepared for the fight to go ahead at London's 90,000-capacity Wembley Stadium.
Former Nigeria boxing chief coach, Obisia Nwankpa has challenged Nigerian-born British world heavyweight champion, Anthony Joshua and his American counterpart, Deontay Wilder to "stop talking" and act like the legendary Mohammed Ali, who traveled around the world fighting his opponents in his days.
"We want to make it public that Deontay wants the fight..."
Promoter Eddie Hearn is not as convinced as his father about the next step, but wants to see Joshua take on Wilder.
Wilder comes off of a spectacular knockout victory over Luis Ortiz earlier in March, and Joshua defeated Joseph Parker this past Saturday to capture the WBO heavyweight title.
Joshua's rise has breathed new life into the heavyweight division.
Appearing on The Breakfast Club radio show on Power 105.1FM, Wilder was asked about whether he has sympathy for anyone he goes toe-to-toe with him in the ring.
"But I think there was a bit of poor refereeing that didn't help".
"The right hand can take you around the block, but a good jab will take you around the world - and that secured another world championship belt", said Joshua.
Wilder, who watched Parker's defeat by Joshua from home last weekend, holds the WBC belt that Joshua so craves to become the undisputed heavyweight champion of the world. Youre going to have to give everything to beat me..
"Just like Dillian said, Wilder, let's go baby, let's go!"
"I know the bookies say I might get a knockout. but forget the hype, Joseph Parker is a world champion".
This morning's heavyweight unification bout between Parker and Joshua has sparked outrage over supposed poor referee decisions, apparent poor count of rounds won, and upset to a lot of kiwi and Samoan fans. Joshua has never left Great Britain for a professional bout, with his last two fights taking place at 78,000-seat Principality Stadium in Cardiff.
Joshua wants to determine for himself if Wilder's side is as serious as Wilder has repeatedly stressed he is to fight Joshua in recent months.
There were also wins for Anthony Crolla, Josh Kelly, Joshua Buatsi and Joe Cordina on the undercard.