Whyte inflicted a brutal knockout on Dereck Chisora before calling out IBF, WBO and WBA champion Joshua, who was ringside at London's O2 Arena.
AJ moved from his commentary position to the ring and suggested a rematch of the 2015 fight, when Joshua beat Whyte, could happen.
But he told Sky Sports: "Dillian's an idiot. You know why? I showed him some respect, I told him, look, I knocked you out clean when we fought but I said let's forget about that because we've both developed, so let's prove who's the better fighter now.
"If Deontay Wilder isn't serious and he's going to fight Tyson Fury and he don't want to become undisputed, Dillian will get a shot. He starts piping up so I said, cool. I'm quite respectful.
"But if Dillian steps in the ring with me, trust me you best believe none of these heavyweights are on my level."
Joshua had been in negotiations with WBA holder Wilder while former world champion Fury also called out his fellow Brit.
Joshua added: "I keep my lid on because I don't want to explode on none of them but I do that business in the ring and if Dillian's serious he can come get this work as well.
"But when the crowd start cheering and saying they want to see Dillian, and if it does happen, I don't want to see no talk when I whoop him and I knock him out of he's an easy touch, he should have fought Wilder.
"Any one of them are welcome to step in that ring with me."
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