At least that's what Tyson Fury is willing to bet £5,000 on as speculation grows as to who Joshua will fight next.
Joshua retained his WBA and IBF belts when he overcame Carlos Takam at Cardiff's Principality Stadium last month.
And a showdown with WBC title holder Deontay Wilder has been talked up since, with Eddie Hearn confirming talks over a potential bout are ongoing.
Parker has been touted as a potential opponent too as Joshua looks to unify the heavyweight division.
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Fury doesn't seem to think Joshua would have much chance of beating Parker though.
"If Anthony Joshua fights Joseph Parker I will bet anybody in the world £5000 cash the [that] Parker will ko him?," Fury wrote on Twitter.
On Monday Parker's promoter, David Higgins, reacted furiously to what he claimed was Joshua's first offer to his client.
"I got this weird email from Eddie's email address, but he must have been hacked," Higgins said.
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Tyson Fury reckons Anthony Joshua would lose to Joseph Parker
"He made the most ridiculously low offer. It could have been the most insulting offer in boxing history.
"To expect 40 per cent is actually quite reasonable, because you have earned it, and it's a unification.
"Of course I have mentioned it [to Joseph Parker] and he just laughed like I did.
Tyson Fury reckons Joseph Parker would knock Anthony Joshua out
"I'm not going to reply, because I don't think it was Eddie Hearn. I reckon someone hacked his account, it was a scam.
"I reckon Eddie respects boxing and I reckon Anthony Joshua wouldn't want to insult Joseph Parker.
"Joseph has worked his way from the ground up and earned the right. Joshua, I think, would understand and respect that, so it can't possibly be AJ or Eddie that made the offer.
"It must be an email hack."