AJ hasn't stepped intot he ring since he was knocked out by Daniel Dubois a year ago, while the Gypsy King's last outing came when he lost on points for the second time to Oleksandr Usyk in December 2024, and though the latter has previously announced his retirement, the Matchroom chairman is still hopeful they'll face one another eventually.
Eddie told Sky Sports: "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."
Joshua branded Fury "dippy" in a recent social media post and Eddie thinks that shows how much the 35 year old wants the fight.
He said: "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."