White confirmed the plans to ESPN on Friday, following an initial report by Brazilian news outlet Combate.
The bout still needs to be negotiated, but both Cejudo and Aldo have expressed interest in the matchup. The promotion is targeting the championship fight for UFC 250 on May 9 in Brazil.
The matchup is a little unconventional in that Aldo (28-6), the former featherweight champion, is coming off a split-decision loss to Marlon Moraes at UFC 245 in December. White, and some other observers, felt Aldo deserved to win on the scorecards.
"I told you guys at the press conference after that fight, this is the fight Henry Cejudo wants," White told ESPN. "I thought, personally, Jose Aldo won that fight, but either way, it was that close. Jose wanted this fight. Cejudo wanted the fight. And who wouldn't want to see that fight?"
Cejudo (15-2) is one of the hottest fighters in the world. The former Olympic gold medalist in wrestling won the UFC's 125-pound flyweight title in 2018 by defeating Demetrious Johnson. He then became a double champion in June by knocking out Moraes for the vacant belt at UFC 238.
Cejudo, who fights out of Arizona, has since vacated his flyweight title to focus on his bantamweight reign. He has made it known he wants his first defense against Aldo.
Aldo (28-6) is actually on a two-fight skid. Prior to the loss to Moraes, he suffered a decision loss to current featherweight champion Alex Volkanovski in May.