Whyte, 30, knocked out Dereck Chisora, 34, last night in what was a rerun of their 2016 classic – with the rematch possibly eclipsing the initial fight for action and excitement.
Promoter Eddie Hearn alluded before the fight the winner could face Joshua, 29, next year as the WBA, IBF and WBO titleist is pencilled in for an April 13 date at Wembley.
After Whyte’s devastating 11th round KO, the 30-year-old called out Joshua, who was commentating for Sky Sports during the show.
But Joshua told Whyte and all those watching on that he would prefer a showdown with WBC king Deontay Wilder or Tyson Fury next year.
Whyte responded by claiming he won’t wait for a fight with Joshua as he looks to build on his own career.
He said: "I'm not going to sit around and wait for him. I'm not going to waste three, four months of my career waiting for him, waiting to hear what he's doing. I ain't got time for that.
"My career needs to progress. There's fighters that sit down and wait two years, waiting for the call.
“I can't do that, time's ticking. I'm 30, I'm about to hit my prime now. I need to act and keep building.
"We were supposed to hear about the Joshua fight after the Wilder-Fury fight. But no, nothing. Nothing yet. I can't sit and wait for that. I've got to plan my future, do what I'm doing.
"My career does not depend on AJ. He's got four of the belts but if I'm mandatory for one or two of them and he doesn't fight me, they will strip him at some point.
"It's only a matter of time. I need to keep working hard, winning fights and it will happen.
"I just hope that I don't get sidestepped for too long.”
Whyte once beat Joshua in the amateur ranks, however, their rematch in the pros in 2015 ended with a seventh round KO win for AJ.
Since that loss Whyte has won nine straight with triumphs over Chisora, twice, and ex-world champions Lucas Browne and Joseph Parker.
Despite Joshua’s wish for Wilder, 33, Hearn fears an undisputed world title fight with the American won’t happen in April.
The promoter tipped Whyte as the most likely candidate to bein the opposite corner to Joshua at Wembley next year.
Hearn said: "I don't believe that Wilder will fight Joshua in April. We'll sit down pretty much immediately [with Joshua and Whyte] and decide whether there is a deal to be done.
"If there is a deal to be done for that fight, there's a very good chance that it will be next.
"I do feel as though he deserves a world title shot and I do feel as though he is either in his prime or quickly approaching it."
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