"It's the fight that everybody wants to see. People want to see Chael vs. Anderson," White said. "Anderson is in this position where he feels like the guy is so disrespectful he doesn't want to give him a shot.
"But Anderson will end up fighting Chael. The answer is yes."
White did not say when or where the fight would take place. Silva is currently recovering from a shoulder injury.
Sonnen nearly defeated Silva during their middleweight title bout on Aug. 7, 2010, at UFC 117 in Oakland, Calif. He dominated Silva for four-plus rounds before submitting at 3:10 of the fifth.
Since the loss, Sonnen has continuously taunted Silva. But after stopping Brian Stann in the second round Oct. 8, Sonnen upped the ante.
"Anderson Silva, you absolutely suck," Sonnen said. "I'm calling you out, Silva, but I'm upping the stakes.
"I beat you and you leave the division. You beat me and I leave the UFC forever."
While the statement increased interest in a Silva-Sonnen rematch, the fight was never assured.
Mark Munoz strengthened his case for a middleweight title shot on Nov. 5, when he stopped Chris Leben in the second round at UFC 138. He expressed his desire for a title shot against Silva, and it seemed he might get it.
But White's recent statement quashes Munoz's hopes temporarily.
Franklin McNeil covers mixed martial arts and boxing for ESPN.com. Follow him on Twitter at www.twitter.com/Franklin_McNeil.