Joshua, who says Fury is on his "hit list", avenged the only defeat in his professional career when he saw off Andy Ruiz Jr. in Saudi Arabia in December, before a bout against Kubrat Pulev was postponed due to Covid-19.
Coronavirus has also caused a delay to the Gypsy King's third fight against American Deontay Wilder, but the appetite for an all British bout to decide an undisputed heavyweight champion remains.
Joshua, 30, told the Sun: "Undoubtedly the fight I want is Tyson Fury - he is holding something that I want, he's on my hit list.
"He says things about me all the time, there is so much back and forth, but Tyson Fury is only relevant the day me and him sign a contract to fight.
"He is a great person and he has done great things in boxing, but until the day we fight that is where it ends and I don't have anything else to say about him. I really want the belt he holds and that is where I stand."
Joshua's win by unanimous decision in Riyadh (above) have him the WBA (Super), IBF, WBO, and IBO heavyweight titles, while Fury claimed the WBC strap after a seventh round TKO over Wilder in February.
Additional reporting by PA