AJ, who holds the WBA, IBF and WBO belts, grabbed the microphone at the O2 Arena, London, to talk about his next opponent.
Whyte called out the 29-year-old champion for a rematch next year – with the Brixton-born fighter desperate for a shot at the big time again.
But Watford's Joshua, who was ringside for the fight with Sky Sports Box Office, refused to commit.
AJ said: “Dillian, let’s forget about that first fight, it was a good fight back then, let’s go again.
"If No1 and No2 are not available, I will do Dillian.
"If anyone deserves it, it is Dillian. If it is not Wilder would fans want me to fight Dillian Whyte.
"If I cannot get Deontay Wilder, he is my target, then it will be Dillian Whyte."
Clearly, Joshua wants to unify the heavyweight division by taking on WBC champion Wilder.
The Bronze Bomber kept hold of his belt earlier in December after his pulsating draw with Tyson Fury.
But the London crowd were unhappy that Joshua avoided another fight with Whyte, whose savage left hook left Chisora sprawled out on the canvas in the 11th round.
Joshua and Whyte met at The O2 three years ago with AJ landing a seventh-round knockout.
Eddie Hearn represents both fighters and has already booked AJ in at Wembley for April 13 – but his opponent is yet to be confirmed.
The unpopular promoter was teased by Joshua when the champ asked for a round of applause for Hearn in the ring which was unsurprisingly met with boos.
But Hearn then said it is a case of "when" not "if" Joshua and Whyte fight again.
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