WBC heavyweight champion Deontay Wilder says he is "ready to come to the UK" for a unification bout with WBA, IBF and WBO title holder Anthony Joshua.
American Wilder, 32, said his team are "ready to meet" the Briton's side for talks - and "the sooner the better".
Barry Hearn, chairman of Matchroom Sport, which promotes Joshua, said negotiations could start this week.
Joshua, 28, beat New Zealander Joseph Parker on points to claim the WBO title in Cardiff on Saturday.
However, a potential Joshua-Wilder meeting is complicated by the fact the International Boxing Federation has ordered a fight between heavyweights Dillian Whyte of Britain and Bulgarian Kubrat Pulev.
The winner would become the mandatory challenger for Joshua's IBF crown.
A bout between Joshua and Wilder would deliver the first man to hold all four major heavyweight titles.
Joshua had said after Saturday's victory that he is in "the most powerful" negotiating position and his side are "serious" about talks.
In a statement on Tuesday, Wilder said: "I want to congratulate Anthony Joshua on his win last Saturday. Anthony, I am so glad we finally heard from you on Saturday and that you want to fight me as your next opponent and you want the fight to happen in the UK.
"I accept that challenge and I am ready to come to the UK for my next fight. There is nothing on Team Wilder's side to prevent me from fighting you next.
"You also said on Saturday that your team is ready to meet with Shelly Finkel and Al Haymon from my side to get this deal done. They are also ready to meet with your team immediately. Let us know when - the sooner the better."
Speaking on BBC Radio 5 live's boxing podcast, expert Steve Bunce said he does not feel the fight "is happening soon", while BBC boxing correspondent Mike Costello added that Joshua needs to go to the United States if he wants to be "remembered among all the great names".