IBF, WBO and WBA champion Joshua confirmed after beating Povetkin that his "number one choice would be Wilder". "My No. 1 would be Wilder".
Asked whether he fancied a rematch by presenter Anna Woolhouse, Whyte said: "Of course I fancy it".
Povetkin's career has been marred by failed drug tests, but after finishing up a drug suspension past year, Povetkin returned to form, knocking out David Price in his last fight to become the mandatory challenger to Joshua's title.
"That is the biggest fight in boxing; Wilder-Fury is a really good fight to see who's the second best heavyweight in the world".
"They will never fight me ever!" Yet Joshua has quietly grown from each performance in ways that may not have been fully realized until Saturday when he held off Povetkin's attacking style by boxing from distance and used quick combinations in close to work his way out of trouble. He's slow, methodical, ponderous at times.
The London 2012 Olympic gold medallist knocked him down with a powerful range of punches that left the Russian in serious trouble but he managed to get up and the Brit continued his onslaught of punches before referee Steve Gray stepped in and Joshua extended his unbeaten professional record to 22-0.
Joshua beat Klitschko at Wembley Stadium last April
According to Fury's trainer, Ben Davison, he's ruled out the possibility of Joshua-Wilder taking place in April.
BBC Sport boxing correspondent Mike Costello: "13 April back at Wembley is an absolute definite. I think the quality of opponent, for all Povetkin has done, for me, the way he was beaten makes it the most impressive display of Joshua's career". You should know better, and Radio 5 should be ashamed of themselves.
"I wasn't looking for the knockout but the instinct told he was hurt. He was moving great, throwing different shots, so it was controlled and he didn't waste anything".
Joshua first wobbled Povetkin with a right hand, followed by a left before the telling left hook and right hand sent the challenger crashing to the canvas.
Paul Hayward, The Daily Telegraph: "These 80,000 sell-outs have become a blessing and a burden for Joshua". And everything to lose.
WBC titleholder Wilder (40-0, 39 KOs), 32, has signed to face Joshua's British rival Tyson Fury on December 1 at what is expected to be an American venue. After that loss, Povetkin won eight straight fights with six of those wins coming by knockout. "Only the most parsimonious will deny him the credit he deserves now".
Tracking the Tropics: Leslie joins Kirk in the tropics
This system could get a boost by Monday as the strong upper- level winds that are now keeping it at bay are expected to diminish. Tropical-storm-force winds extend outward from the center up to 35 miles (56 kilometers) to the northwest.