Oleksandr Usyk's team see "no visible obstacles" to agreeing a fight with Anthony Joshua in the next few days.
The WBO ordered Joshua to defend his belt against mandatory challenger Usyk after the breakdown of his planned undisputed title fight with Tyson Fury.
Joshua and Usyk were given until May 31 to negotiate terms before the fight will be decided via purse bids. But Joshua is also considering other opponents, his promoter Eddie Hearn has said.
Joshua holds the IBF, WBA and WBO titles but his desired opponent Fury was told to defend his WBC belt against Deontay Wilder by a court of arbitration.
"We are in the middle of negotiations now and things look optimistic," Usyk's promoter Alexander Krassyuk told Sky Sports about talks with Joshua's representative Hearn.
"As long as I am informed there are no visible obstacles to the deal not to take place, hopefully, it will be completed within the rendered timing."
Usyk's team had previously said the fight would take place in the UK in August and Wembley Stadium was an option to host it.
Hearn told Behind The Gloves about Usyk: "It is the fight that is most likely for us.
"We are talking to other people, as well, about other fights.
"The aim is to be undisputed. All AJ has done is to box off mandatory fights to keep the belt. How much longer does he have to do that?
"You never get the freedom to do what you want. In an ideal world we'd like to do what Saul 'Canelo' Alvarez has done - have three fights in six months.
"But it's about defending the belts. He wants to become undisputed.
"He doesn't want to lose the belts but his hands are always tied."
Fury and Wilder's trilogy fight is planned for July 24 in Las Vegas. The first fight was a draw before Fury ended Wilder's title reign and undefeated streak in the rematch.
"Wilder, this contract is signed," Fury said.
"You're getting smashed. When I say smashed, I mean smash, smash, smash, bang.
"You're getting knocked out. End of. One round, you're going. I've got your soul, your mojo, everything."
When will Joshua vs Fury happen?
Joshua's promoter Hearn suggested the undisputed title fight, which was planned for August in Saudi Arabia, could be rescheduled for December if they each win their next fights.
"The world now sees you for the fraud you are," Joshua posted on social media towards Fury.
"You've let boxing down! You lied to the fans and led them on. Used my name for clout not a fight.
"Bring me any championship fighter who can handle their business correctly."
Fury replied: "You are more full of [rubbish] than [promoter Eddie Hearn]. Your full team knew there was an arbitration going on, it was out of my hands!
Joshua hit back: "If there was an arbitration going on, why announce to the world we are fighting! The fight was signed!"