Tyson Fury and Anthony Joshua could fight twice over the next 15 months - assuming they each win their next fights.
The British heavyweights hold all four world titles between them after Fury's seventh-round stoppage of Deontay Wilder .
The pair had hoped to clash this summer but Wilder has exercised his right to a rematch which is set to take place on July 18 in Las Vegas.
In the meantime, Joshua will defend his three belts against Kubrat Pulev at the Tottenham Hotspur Stadium on June 20.
Assuming there is no upset in either fight, talks will then intensify over an undisputed clash.
"The great thing is that [Fury vs Wilder] is in July and we box in June," Joshua's promoter Eddie Hearn told Sky Sports News .
"Now our intention, and conversations are ongoing, is to finalise the Fury vs Joshua fight for December of this year. There's no reason not to get that contracted now, subject to both guys winning in the summer.
"We had numerous conversations with Bob Arum at Top Rank over making Joshua vs Fury.
"But we know that once Wilder exercised that rematch clause, that fight would be made. We understand Wilder wants to win his belt back.
"The proudness and ego of Wilder meant it was very unlikely. He's not stepping aside, he wants this rematch with Fury. 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."
Saudi Arabia has emerged as the most likely venue for Fury vs Joshua after it played host to the latter's revenge win over Andy Ruiz Jr last December.
But Hearn insists he will do all he can to bring the fight to the UK.
"We must try and do that fight in the UK," he added. "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."
