As evidence of the moneymaking potential, the Los Angeles Times' Lance Pugmire reported in May that Finkel and Al Haymon were prepared to give Joshua $50 million guaranteed if he was willing to fight Wilder in the United States.
"We have agreed to the terms that Eddie has put out to us for a fight in the UK", Wilder was quoted by ESPN as saying.
"They offered and we accepted", Deas said, adding that they would push for a signed contract as early as Tuesday.
Assuming the details are finalized and the fight announced, Joshua vs.
Hearn told Sportsmail: 'We made him (Wilder) an offer four weeks and now they have come back via social media accepting terms and wanting to proceed to contract.
Russian Alexander Povetkin is the WBA's mandatory challenger and is close to a deal to fight Joshua, although Joshua could face Wilder first if Povetkin is able to fight the victor. The fact that both men are the height of National Basketball Association stars and have devastating knockout power will make the bout, should it happen, a must see for fans - even casual fans. The $50M offer for him to fight me next in the U.S. is still available.
"If they keep their word, then we've got a fight", Deas said. We made this offer about four weeks ago and I don't know if he's come back because he's heard we're close to closing the Povetkin fight or whether he wants the fight, but either way he's going to be getting a contract from us ASAP.
"I think Wembley is where Anthony Joshua wants it to take place". It's up to them to choose US or United Kingdom.
Hearn told Sky Sports News it is the only way to find out if the WBC titleholder Wilder is serious about fighting Joshua even though reports out of the United States on Monday suggested he had accepted a two fight deal with the 2012 Olympic champion and now holder of the WBA, WBO and IBF belts.
Should Joshua, 28, fight the American next, the victor would become the first heavyweight to hold all four recognised world titles at once.
The offer also includes a rematch clause, which Joshua and his team insisted on, and Wilder is happy to accept that also.