Anthony Joshua and Tyson Fury remain at the centre of talks to stage an undisputed title fight in 2020, and promoter Eddie Hearn has described progress as "all positive".
Fury captured the WBC title by spectacularly beating Deontay Wilder meaning both recognised heavyweight champions are British - Joshua holds the IBF, WBA and WBO belts.
Talks are underway between Joshua's promoter Hearn and Fury's US-based promoter Bob Arum to pit them against each other later this year, although both champions must come through separate fights in the meantime.
Joshua will defend his gold against mandatory challenger Kubrat Pulev on June 20 at the Tottenham Hotspur Stadium, live on Sky Sports Box Office, then Fury and Wilder are expected to meet for a third time in July.
"There's no reason why a deal can't be done now to lock in Joshua and Fury for that November-December date," Hearn told Sky Sports.
"Conversations are ongoing with Bob Arum and are all positive."
Hearn had previously said: "The undisputed fight must happen in 2020.
"Joshua and Fury are certainly going to be boxing twice [or a] trilogy. That's part of the deal that we are looking to do ASAP - a two-fight agreement with Fury and Arum at the end of this year then summer 2021.
"We must try and do that fight in the UK. Ask AJ and Fury where they would like it, and they would say the UK. We know there will be huge offers from around the world. Our priority is to try and make this fight in the UK.
"There will be two of these, maybe three, so certainly summer 2021 we'll get one in the UK. I would love to make the first one in the UK because we've got two British world champions who will fight for the undisputed title - this is never going to happen again. To do it in the UK would be very special."
Dillian Whyte will fight Alexander Povetkin on May 2 in Manchester, live on Sky Sports Box Office, defending his status as WBC interim champion and mandatory challenger.
Whyte first became No 1 contender with the WBC in November 2017 but has still never challenged for the world title, although Hearn believes his wait could eventually be worthwhile.
"Whyte was mandatory for so long for Wilder, it was always our aim for Whyte to beat Wilder then make him against Joshua for the undisputed title," Hearn said.
"Now if Joshua fights Fury, the mandatory is Whyte.
"You will have an undisputed fight between two Brits then another Brit coming into the mix to fight for the undisputed. The heavyweight division in Britain is flying!"
Whyte said: "I'm not thinking about Tyson Fury, what's happening with him, I'm just thinking about Alexander Povetkin, because he's dangerous and he's going to want to come and fight and leave it all on the line.
"That's just in his DNA. We're very similar in that mindset in that we come and give it our all, so I'm just focused on him. We'll see what happens on May 3. We'll have a chat about Tyson Fury and that. Now I'll put that on the backburner and just focus on Alexander Povetkin for the next eight weeks."