Fury, 37, has come out of retirement for the fifth time in his career to get back into the ring at the Tottenham Hotspur stadium and is looking well beyond the weekend.
"I've got Arslanbek Makhmudov to think of on Saturday night, but all going well (Joshua is) the fight I want next," he told BBC radio on Wednesday.
"I know he just had his fight with Jake Paul, whatever... a fight's a fight, really. So yeah, I'll be ready for that straight away after this."
Joshua, 36, last fought in December when he dealt American Jake Paul a reality check with a savage sixth-round knockout in Miami.
A few days after that, the former WBA, IBF and WBO champion was taken to hospital in Nigeria following a car accident that killed two close friends.
American former WBC world champion Deontay Wilder has also called out Joshua for a long-awaited matchup after beating Briton Derek Chisora on a split-decision last Saturday.
Fury, who has not fought since losing to Ukraine's reigning world champion Oleksandr Usyk in December 2024, dismissed the idea of that happening.
"I've never seen two men slide as much as these two," he said of the Wilder vs Chisora bout. "They look like a couple of club fighters from a white-collar match in a local leisure centre. It was sad for me to watch."