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The 43-year-old is a former UFC heavyweight champion and Jones, who is set to step up to that division, wants to square off with 'The Beast Incarnate.'
However, current champion Miocic insists he should be the man to face Lesnar.
"A hundred per cent I think so," he told Michael Bisping on the Believe You Me podcast.
"Listen, I just think about it more and more I do think 100 per cent if anything I would get the Brock Lesnar fight first or be asked first.
"I didn't know [Jones] called the shots. I didn't know that."
'Bones' relinquished his light heavyweight title last month and is ready to start the next chapter of his career.
He he wasted no time in responding to rumours of Lesnar's potential return.
On Twitter, Jones called him out with the simple message: "Brock I'll beatcho ass too."
UFC president Dana White admitted he would consider bringing Lesnar back if he was "seriously interested" in fighting.
When asked about Lesnar vs. Jones, White replied: "It would be a good introduction for Jones into the heavyweight division. If they wanted to do it, I would do it."
One man who isn't thrilled with a potential Lesnar return is former rival Alistair Overeem.
Overeem, who defeated Lesnar at UFC 141 back in 2011, has slammed a potential comeback and claimed "nobody cares."
He told TMZ Sports: "I beat him up.
"So if somebody wants a rematch, it would be him. I already did it. Why would I chase him? Who cares about Brock? Which fans? He's not coming back.
"He's 43 years old, he's flunked tests, it's over with him. He's not coming back. Last time the waived the testing for him and still he got into trouble. It's been a debacle. He's not gonna come back. Listen, if he does, all hats off to him, but I don't think he's gonna come back."
Lesnar stepped away from the promotion after losing to Overeem but returned in 2016 to battle Mark Hunt at UFC 200.
While he emerged the victor, the bout was changed to a no-contest after Lesnar failed drug tests prior to and following the fight.
Featured Image Credit: PA Images
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