Eddie Hearn told Sky Sports he would "kick himself" if Anthony Joshua and Tyson Fury never fought, calling it the "biggest fight in boxing".
Joshua has not boxed since being knocked out by Daniel Dubois a year ago, while Fury's last outing was in December 2024 in a second successive points loss to Oleksandr Usyk.
Fury announced his retirement after that defeat but Hearn is hopeful the unified heavyweight champion will launch a comeback.
The Matchroom chairman said: "It would be a real, real shame if Tyson and AJ never fought.
"I don't really have many regrets but I think we would always kick ourselves if we never saw that fight. It's the biggest fight in boxing.
"You can't even compare anything that we've done so far - Carl Froch-George Groves, AJ-Wladimir Klitschko, Benn-Eubank. This is just completely different.
"It shuts down the country. They're two very different but great fighters, two great personalities, two completely different individuals. For me, it's a must."
"Tell me a bigger fight in boxing? It doesn't exist. It's not just fighting and beating Fury for AJ. It's just giving the British public what they've wanted for so long."
'AJ is fired up and we still believe he's got a lot to give'
Joshua called Fury "dippy" during a recent social media post and Hearn insists that shows how much the 35-year-old wants to fight Fury.
Hearn says Joshua would be looking for a tune-up bout in January or February and expects Fury to want one, too, before a potential all-British showdown.
He added of Joshua's Instagram post: "I love it, I like to see it. AJ's always a guy who has held his tongue. I think now as he comes to the back end of his career, he's almost like, 'why not?'
"He wants this fight. We want the fight, we're ready to go, we're ready to talk about it. This isn't goading Tyson Fury, it's just stating facts.
"The good news is that AJ is recovered, injury-free and ready to start training camp. And he has got the bit between his teeth to get back in big fights in the heavyweight division. He's fired up and we still believe he's got a lot to give.
"You can see across Fury's social media, he's training, which gives you hope. I think people around him feel like he'll return, but you never know."
Asked whether fighting Joshua and losing represents a risk to Fury's legacy, Hearn said: "I'm not really a kind of legacy-damaged kind of guy. Ultimately you take the fights and if you're good enough you win, and if you're not you don't.
"I don't think you should worry about gambling on your legacy. The legacy comes through giving people great fights and fighting anybody.
"Personally, AJ wants to knock Fury out. But from a legacy perspective, the legacy is fighting everybody. AJ wants to be remembered as a guy that fought everybody.
"We definitely could have, we maybe should have, swerved Usyk, but the legacy comes from giving people great fights.
"If you want to be critical of Fury's CV, it's very easy. But at the same time, he's a tremendous fighter. Let's find out who is the biggest name and best Brit of that generation."
