Wilder's co-manager Shelly Finkel told ESPN they had agreed to the latest terms offered by Joshua's promoter Eddie Hearn.
World heavyweight champion Deontay Wilder claims he has agreed to fight Britain's Anthony Joshua in the UK.
The Joshua-Wilder deal, should it come to fruition, will consist of two fights, the first being held in England, the second in the United States.
According to Pugmire, Wilder's and Joshua's respective teams were quibbling over the location of the fight, with Wilder's camp wanting it in the USA and Joshua's side preferring the UK.
"They gave us an offer, we were hoping they'd accept the U.S offer instead because there's so much money but instead since they haven't we've decided that if you don't want $50m then we're willing to come the United Kingdom and take your offer".
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.
"Now we will see if they live up to it or if they try to go through with the fight with [mandatory challenger Alexander] Povetkin first".
"The $50M offer for him to fight me next in the U.S. is still available", Wilder said.
"We see this as a Wembley fight and we're quite limited in that respect", said Hearn.
Starsport understands it is considerably more than the £9.3m that Hearn originally offered Wilder back in early April.
Yet it appears a breakthrough has come in negotiations between IBF, WBA and WBO champion Joshua and WBC title holder Wilder.
"If they keep their word, then we've got a fight", Deas said.
The 28-year-old Joshua (21-0, 20 KOs) won a world title in 2016 and has made five defenses, including a 10th-round knockout of former longtime unified world champion Wladimir Klitschko in the consensus 2017 fight of the year and unifying three belts with the win against Parker on March 31.
Last night, he tweeted: "Breaking news for all you for all you Anthony Joshua fans". But we need to get the contract back from Deontay Wilder - then we will know if this is bluster or if he is serious'.