Joshua, who has Nigerian blood, and Briton Fury have both signed a contract for an undisputed world heavyweight title fight, although a date and venue have not been confirmed.
While Joshua holds the World Boxing Association, International Boxing Federation and World Boxing Organisation titles, Fury is the World Boxing Council champion.
“Tyson Fury, who many do believe is No.1 because Fury beat Wilder, and he’s the lineal champion, but I think it’s the perfect time for Anthony Joshua,” Haye, a former world champion in the cruiserweight and heavyweight categories, told Sky Sports News.
“Tyson Fury is on such a high. The victory over Wilder made him look a million dollars, his confidence will be sky high and I genuinely think Fury and his team don’t rate AJ as highly as they should do.
“That, in itself, causes potential issues.”
Fury punched American Deontay Wilder to submission in the seventh round to claim the WBC belt in February 2020, but Haye believes Joshua is a very different prospect.
“If Tyson Fury attacks Anthony Joshua in the same manner, in which he did in Vegas against Deontay Wilder, I don’t believe it works in his favour,” 40-year-old Haye, who retired in 2018, added.
“I believe he’ll be too open, too wide and someone as fast, athletic, and as skilful as Anthony Joshua will be able to punch right through the middle and take him out, and take him out early.”I know it’s a controversial prediction.”