The New Zealander lost his WBO heavyweight belt to Joshua back in 2018, but both of them have mounted comebacks after career setbacks.
Joshua has three wins in a row after twin defeats to Oleksandr Usyk, while Parker has five consecutive victories after a 2022 defeat to Joe Joyce.
His last win came against Zhilei Zhang in March this year, and speaking in a statement, he discussed his good form.
He said: “I’ve been boxing 11 to 12 years and I’ve found what works for me, the formula I’ve got, Andy Lee head trainer, George Lockhart and the work that we’ve been doing together.
“It’s been a grind ever since we’ve linked up the three of us. But everything is working very well and whatever we’re doing we want to keep it up.”
Discussing a rematch with Joshua, he explained: “There’s a lot of people that want to fight Anthony Joshua. I feel like with what I’ve done I can be in a position to fight him.
“To be honest, it’s not really about what I want and what he wants. It’s what everyone else wants and a lot of fights are happening in Saudi Arabia.
“With the belts all being (held by the) undisputed heavyweight champion of the world, there’s a rematch clause in place, but again these things may or may not happen.
“You never know how things are going to unfold. So we’ll see. We’ll see what happens. But you’ve got Anthony Joshua… I let whatever happens happen and whatever fights they lock, they lock in and I’m ready for whoever.”
Olaitan Ibrahim