Potentially within four months, the 28-year-old Brit could be the first undisputed world heavyweight champion since Lennox Lewis in 2000, and the first boxer to hold all four belts in the division - WBA, IBF, WBO and WBC.
"We don't mind the hype, we like the criticism, but say it to us!"
It is reported that the UFC wants to become more heavily involved in the sport of boxing and the next step would be to lure Joshua away from Matchroom Boxing and promoter Eddie Hearn after successfully helping organise the much publicised Conor McGregor v Floyd Mayweather bout.
And while a potential Joshua-Parker match may not be on the horizon, Higgins believes that Parker would have the advantage if it ever came to pass.
"If he was serious about the fight, we'd do serious negotiation", Joshua said on Wednesday.
"I definitely know there'll be blood".
"If he offered me 10 times more money to fight than what I am looking at in the United Kingdom, I would go there to fight him".
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First of all, however, Joshua has to deal with Parker, a tough New Zealander who arrives in the United Kingdom with a 24-0 record - 18 of them knockouts - but the least envied of the four belts. There's a lot of bluster with Deontay but he's not an idiot. "There are rumours that Parker has been injured for the past two or three fights but now is injury-free and looks unbelievable in training". That's added pressure. I don't think he feels it though.
"I'm learning. Fight week is as important as camp".
There has been much debate over what Joshua's weight will be for the showdown, and the star has confirmed he intends to tip the scales lighter than for previous fights at "112kg max", or 17st 8lbs.
Joshua has won all 20 of his professional bouts by knockout so far.
"I should be a lot quicker and outwit him", he said.