Frank Warren is confident Anthony Joshua and Tyson Fury will finally meet this year in either May or June.
However, the legendary promoter again stressed the COVID-19 pandemic made it extremely unlikely the fight will happen in the UK this year.
The first undisputed world heavyweight title fight since Evander Holyfield and Lennox Lewis locked horns in 1999 looks closer than ever after the WBO reached out to Oleksandr Usyk.
With the Ukrainian likely to face Joe Joyce for the interim strap, it leaves Joshua and Fury free to duke it out for the WBA, WBO, WBC, IBF and Ring Magazine titles.
Fears about the fight not being in the UK, despite two British fighters taking part, had intensified in recent weeks given the alarming surge of coronavirus and yet another national lockdown gripping the nation.
And although Warren admitted the fight may not happen on these shores, the first of two blockbuster bouts could be coming in just a matter of months.
“Everybody wants the fight between Tyson and Anthony Joshua,” Warren told Jim White on talkSPORT.
“That is what the agenda of everybody who is concerned is and we will do all we have got between us all to make sure it happens.
“That’s the fight everybody wants to see and, whatever the result of the arbitration, if and when we get some result we will deal with it as and when.
“I honestly believe the next fight will be the two guys, nobody can predict anything at the moment, can they? We are in the middle of this pandemic, we all thought by now we would be having live events in the UK.
“If you had asked us this four months ago, that was where it was heading. 2021 it was all going to be over, when in fact it is looking worse.
“So it is wherever the best offer comes from; there have been a few offers made, I’m not going to go into where they have come from, but everybody will collectively look at them and collectively the decisions will be made.
“But the fight, we are hoping to get it on and, if we are being realistic, it will be some time in May or June.
“I hope that in the next few weeks it is over the line. We are supposed to be getting some sort of draft agreement this week and it will be a two-fight deal.”