Miocic, 38, will defend his title in a rematch with KO machine Francis Ngannou at UFC 260 this weekend.
But he would then consider switching from the cage to the ring to take on either of the Brits who are due to meet in an undisputed clash this summer.
Asked on ESPN why he wanted to fight Joshua or Fury, Miocic said: “It’s a different combat, boxing is all about technique.
“It’s more of a fair fight (than if they fought in MMA); we both fight standing but we can kick and take down, and they’re not used to that.”
Miocic was first crowned heavyweight champion in 2016 when he knocked out Fabricio Werdum in the first round.
He made three successful defences against Alistair Overeem, Junior dos Santos and Ngannou before he was dethroned by Daniel Cormier.
Miocic exacted revenge on Cormier before winning their trilogy fight last August.
And he expects Ngannou – who is riding a four-fight win streak, to have improved since their first meeting in 2018.
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“It won’t be nothing like the first fight because he’s definitely gotten better and so have I,” Miocic told MMA Fighting.
“A lot of things are going to change. I’m trying to make it a more one-sided fight, and of course try to end it early, but he’s gotten better. The man hits hard and it’s the heavyweight division so anything can happen.
“He’s got a great coach and a great team and they’re definitely working with him, making him better. He’s definitely gotten better but so have I.
“I think whoever implements their game plan the best is going to win. He’s definitely gotten better but he’s also got that one factor that everyone thinks he hits hard and he does hit hard. You’ve just got to watch out for it.”