Fury has called out former UFC champion Francis Ngannou to a mixed-rules bout in the cage before.
He proposed a stand-up bout, contested with the smaller 4oz MMA gloves but under boxing rules.
But UFC legend McGregor has heard one too many of Fury’s broken promises to take the challenge too seriously.
He said: “Is Tyson willing to step in the f****g cage or what? He’s saying he would, Tyson says a lot of things.
“I love him, he’s a mad, mad thing Tyson. And I’m excited to see him go.”
Fury, 34, is currently faced with forgoing a summer return fight with available opponents limited.
It came after he saw talks to face Oleksandr Usyk, 36, in the heavyweight division’s first four-belt unification bout collapse.
But boxing bosses in Saudi Arabia are looking to revive the historic fight as part of a series of tournament-style bouts.
Eddie Hearn revealed there is a plan in place to have Fury fight Usyk on the same night as Anthony Joshua, 33, against Deontay Wilder, 37.
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And McGregor probed the promoter at his Black Forge Inn pub in Dublin, just days out from Katie Taylor’s homecoming fight.
He said: “What’s the old craic with the old Saudi, is that four real? With the four? I know you want the fight. Saudi want to do it?
“Interesting isn’t it the Saudis, do you reckon it will happen?”
Hearn: “It’s a lot of money. There’s three people that will do it. We’ll see what Tyson Fury thinks.”
McGregor lost his boxing debut in 2017 to unbeaten great Floyd Mayweather, 46, but fancies fighting Mexican icon Canelo Alvarez, 32.
Although he joked Hearn would have to settle for a co-promotion such is the UFC icon’s superstardom.
McGregor said: “You know the level I’m at, at best co-promote! At best co-promote.”
