Joshua holds the IBF, WBA and IBO heavyweight titles, while Parker holds the WBO crown.
With melodramatic music playing in the background, Wilder says: "Anthony Joshua, you know I'm coming for you".
"It's now a question of the deal and money".
After initial talks they agreed they would ask their fighters who both gave them the green light to try to arrange a bout, likely to be in the United Kingdom in March or April.
He added he had also been in talks with Wilder's camp. The American knocked out Bermane Stiverne in NY last Saturday and then accused Joshua of "dodging" a showdown.
"Wilder's crew put a figure on the table that wasn't enough".
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"They've offered us a deal, we've agreed, we're ready to go, so if the fight doesn't happen it' rests exclusively on Joseph Parker", Clark told AAP.
Wilder, who described Fury as the "King of England" then responded by saying Joshua is the man they both want to fight.
He also revealed that WBC champion Deontay Wilder shouldn't be discounted and they were prepared to chase him if Joshua short-changed them.
Sky Bet make Joshua the odds-on favourite at 2/5 to win a potential fight between the pair before the end of 2018.
"The starting point for negotiations is obviously 50/50 but we would acknowledge that Joshua, if the fight were to happen in his home nation, he has a big fan base there".
"We all saw that Joshua could not hurt Takam".
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The 32-year-old knocked his opponent out in the very first round after landing a flurry of devastating punches.
"I think the guy is there for the taking and I want us to get in front of him before someone else beats him".
If the Joshua bout did not come off then Parker could fight unbeaten Australian Lucas Browne instead, Higgins said.
CEO David Higgins told media on Wednesday that the fight was one of several options on their table, and the one they are the most interested in working towards for early 2018. "There is no deal. We have loosely agreed terms and principles. and it is possible if we decide it is the best option".
Parker has just started a six-week camp with Barry in Auckland, opting not to fight before Christmas and that has given Higgins time to work some magic.
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