"The UK is the spot right now for boxing and it's the hottest place to be for boxing," he told the UK's skysports.com. "There is a lot of great heavyweights and a lot of great fighters there."
Parker and Joshua have similar records - Parker has won all 17 of his professional fights, 15 by knockout, and Joshua has won all 15 of his bouts by knockout - and both have similar rankings. Joshua is ranked as high as No 2 by the WBC and WBO, with Parker No 3 on the WBO list and No 6 with the IBF.
His minders will consider their next steps carefully but Parker was hardly shying away from the prospect of a bout with the 2012 Olympic champion.
"I believe that Anthony Joshua is a great fighter and he's doing very well on that side of the world," he said. "I've been following his progress and what he's been doing. It makes me a little jealous, knowing that there are a lot of heavyweights in the UK and there is a lot of great fights for everyone there. In New Zealand and Australia, we don't really have the other heavyweights to contend against.
"I believe if we keep doing well and we keep winning, probably in the future we can meet up somewhere. I definitely have a lot of respect for him and his team. We are taking the same paths in what we're doing in our careers.
"It will definitely be explosive and you have to feel that if I fight with Joshua, we'll definitely put in the work, train hard and it's a big fight for both of us, but I believe it's a fight that can happen in the future.
"We've both got good records and good knockout power. It will be an exciting fight for the future.
"If you have two big heavyweights in a ring and one lands a big punch, then it can change anything. It depends who is more ready on the night."