Although the 25-year-old refuses to overlook Fury, he knows that a fight with WBA and IBF champion Joshua can happen down the line, especially with the carat of his WBO world title.
Speaking to Sky Sports News HQ, Parker said: "At first I have Hughie Fury and I am not going to look past him, but I would love the Joshua fight.
"Joshua is always improving and looked great against Klitschko last time out, he's a clever fighter who wants what I have.
"He's got two titles but there are two more in the division and I have one of them. If he wants to unify the division, he has to face me or (WBC Champion) Deontay Wilder - I would love to set up a fight.
"I back myself against any heavyweight, I train hard, focus and believe I can beat anyone out there. He believes he can beat me so let's get it done."