Some have expressed disappointment that a unification fight with Parker will come before one against Deontay Wilder, the WBC champion.
And Joshua hopes Wilder recognises that he is a greater attraction in the United Kingdom than the American is in the USA and agrees to cross the Atlantic for what would be a big showcase occasion.
Joshua said: "If he was serious about the fight, we'd do serious negotiation". If he wants to be a part of this and jump on the train and come to the United Kingdom, he has to be realistic and stop living the fantasy. We expect him to be lighter than the Carlos Takam fight.
Eddie Hearn, AJ's promoter, is open to the possibility of a two-fight deal with the USA heavyweight to hold bouts in both the United Kingdom and the States. That is all we are saying, be realistic in negotiations.
GETTY IMAGES Anthony Joshua was under the glare of the cameras as he started training following a media session ahead of his fight with Joseph parker
"I know where I am going with my career".
Laughing and joking, Joshua couldn't have been more laid back 10 days out from heavyweight unification fight as he put on a show for the media in the gym used by Britain's Olympic boxers, his body looking as chiseled as ever.
Aware of the quality of the unbeaten New Zealander, Joshua predicted the fight was going to be extraordinary.
"Every fight and training camp has been something to learn from". "Behind the scenes they're different, a lot of the things that they say are different".
He spoke of Wilder being an unrealistic negotiator - "he has to stop living in a fantasy land" - but Hearn, sitting alongside him, said it is a fight that somehow will get made. "In terms of how I'm feeling, in terms of my weight, I'm comfortable", he added.