White said there was no way he could argue against booking the light heavyweight title fight.
"When the fight (against Paulo Costa) was over, I was like 'I'm going to have to sit down with this kid and convince him why he needs to fight Whittaker'," White said at a media conference on Sunday.
"Then Whittaker comes out and says he doesn't want to fight him. That's the craziest s*** I've seen, so there's no arguing with Israel now."
While there has been no timeline given for the fight, it would be in the first quarter of 2021, with Poland's Blachowicz indicating he would welcome a bout against Adesanya in March.
Adesanya has torn through the middleweight division since making his UFC debut in 2018, with nine wins - seven of those against fighters currently ranked in the top 15 of the division.
The bout will give Adesanya the opportunity to become the fifth dual champion in UFC history should he get past the powerful Blachowicz.