Two prickly personalities have once again been drawn into regular rounds of verbal jousting this season, with insults emerging from both Old Trafford and Stamford Bridge.
Neither has shown any sign of backing down, with past misdemeanours and touchline antics among the topics of discussions to have generated barbed comments.
Mourinho and Conte are now set to lock horns once again in the dugout on Sunday, when Chelsea travel to Manchester, but Matchroom Boxing supremo Hearn – who boasts the likes of Anthony Joshua and Kell Brook on his books – would welcome the opportunity to present two heavyweight personalities with a more suitable stage on which to iron out their differences.
"They are both very passionate, I would like to do the fight, we would make a lot of money, but I think they should stick to the football," he told The Sun.
"I see them on the sidelines very regularly and they are both very fiery and passionate, it has all the makings of a great fight.
"It’s hard to beat the Italians for style.
"But Mourinho has been to the boxing and might have learned a few things from Anthony Joshua.
"He has come to a few fights and sits there on his own and might have learned a bit, he has an aura about him too.
"But Conte has the style."
Pressed to pick a winner between Portuguese and Italian grit, Hearn added: "Overall I have to go with Mourinho, I think he is the guy.
"I am not sure we could ever actually get the fight made - can you imagine trying to negotiate terms with them two!"
With a fight unlikely to happen, a global football fan base will have to make do with a Premier League encounter at Old Trafford which promises to deliver as many fireworks off the field as it does on it.