"I like the sound of fighting in the United Kingdom, but if there was a healthy offer or something on the table, then it would make sense to go (to America), but there hasn't been that".
The undefeated champion was satisfied with how his tactics worked against Parker, as he comfortably kept the New Zealander at bay for much of the fight to triumph 118-110 on two cards and 119-109 on the other. "It is a fight Anthony Joshua really wants and I think he wants it this year".
"I would love to have another go".
"My strategy in there was to stick behind the jab", said Joshua.
"This was about boxing finesse". Haven't decided yet how I will win by knockout or on points.
But, thanks to Parker's reactions and counterattacking skills, one of the sport's biggest punchers barely landed a clean shot with his big right hand.
Joshua who put his WBA and IBF titles on the line has now added the WBO's strap to his two belts to unify the division in what is his third stadium fight in succession.
WBC title-holder Deontay Wilder, who has found himself in some hot water this week, could find himself next up for Joshua and that fight, which would decide the undisputed heavyweight champion of the world, could well take place before 2018 is out although both Wilder and "AJ" have mandatory challengers in front of them.
And he wants to stay in Britain to complete the set.
"We will ride our wave while we are here, and we will do what is right for us". They hugged after the final bell, though Parker knew he had been beaten.
Although Joshua went the distance against previously unbeaten Parker, he gained emphatic victory margins on all three judges' scorecards as a stellar career continues at pace. "It's been a good experience being here and I'm thankful for the opportunity".
He may have tougher fights on his horizon but, for now, Joshua is sitting pretty at the top of heavyweight boxing. "(Wladimir) Klitschko, 11 rounds, (Carlos) Takam was 10 so, I've always been in the realms of going 12 rounds if we need to and today was the first time and we covered it well so on to the next, no", said Joshua.
In the chief support bout in Cardiff, Joshua's compatriot David Price was brutally and chillingly knocked out by Russian heavyweight Alexander Povetkin. It is not time to sit back and enjoy the ride, we have got to be ready for the next one. The result was emphatic, though.
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