0125 GMT September 20, 2019
Joshua takes on Parker at the Principality Stadium in Cardiff on March 31 with three world titles on the line, Mirror reported.
And the Brit is confident he will leave the ring with the New Zealander's WBO strap, along with his own WBA and IBF belts.
Joshua said, "I took my time last time out [against Carlos Takam] because I wanted to set up a good 2018. It's about making history now, it's an honor to be up here with another world champion.
"I take everything with a pinch of salt, I don't know what to make of Parker. I'm looking forward to the challenge, not only from a physical standpoint but also from a mental one.
"People have used me getting dropped by Klitschko as a PR stunt. I've been dropped three times but I learned from the adversity and that it will take more than a human to stop me. The other rumors are fake news."
Parker successfully defended his title against Hughie Fury last year and is looking forward to returning to these shores.
He said, "I'm looking forward to leaving here tomorrow and heading back to Vegas to start camp. I've watched Joshua for a long time, I know his strengths and his weaknesses. I can't wait for this fight."
Ringside seats for the highly-anticipated clash between Anthony Joshua and Joseph Parker will cost fans as much as £2,000.
Promoters Matchroom revealed the ticket prices for the monumental battle on Tuesday morning with fans able to snap up their seats from next week.
Tickets for the highly-anticipated clash range from £40 to £600 with VIP entrance, giving fans the best view in the house, due to set them back £2,000.
The fight is expected to sell-out with Joshua's last trip to Cardiff, a 10th round stoppage of Takam, taking place in front of nearly 80,000 fans in the Welsh capital.