Matchroom boss Hearn is believed to have made a counter offer, which would see Wilder challenge Joshua in his backyard and take home a smaller fight purse.
ESPN's Dan Rafael later quoted Shelly Finkel, Wilder's co-manager, as saying that the Wilder camp had agreed to terms with Joshua manager Eddie Hearn on a fight in the United Kingdom this fall, possibly as early as mid-September.
If everything agreed in discussions is included and they are happy with the date and venue, then Wilder will sign for the money-spinning bout.
Wilder's co-manager Shelly Finkel told ESPN they had agreed to the latest terms offered by Joshua's promoter Eddie Hearn.
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Complicating matters is that Joshua is already due to take on WBA mandatory challenger Alexander Povetkin.
If the Wilder fight is next up for Joshua, then the original plan of September 15 is now highly unlikely due to the lack of time involved, as well as the USA television clash with Canelo Alvarez's return from a drug's ban.
"We see this as a Wembley fight and we're quite limited in that respect", said Hearn. "It's up to them to choose".
The prospect of setting foot inside the squared circle and a potential fight with Wilder - the WBC heavyweight champion of the world - was put to Jones by a fan during a Twitter Q&A earlier this morning.
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Joshua, who won his first world title by stopping Charles Martin in 2016, scored his biggest victory to date the following year by rising from the canvas to knock out former champion Wladimir Klitschko in front of 90,000 spectators in London.
The offer also includes a rematch clause, which Joshua and his team insisted on, and Wilder is happy to accept that also.
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. Then they came back with a much, much, much smaller offer for Deontay, which would have been even less than Deontay would have made in the United States, and wanted him to still travel to the U.K. for the fight.
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Coming back from two-sets down proved to be a challenge too far for a man not used to contesting best-of-five-set contests. After a gruelling and protracted struggle, Thiem finally regained control when Cecchinato netted a tired forehand.