Cormier, the UFC heavyweight champion, has been outspoken about wanting to fight the WWE superstar before he retires from the sport. Lesnar lost his WWE Universal Championship belt to Seth Rollins at Wrestlemania last week.
The next logical step for Lesnar, it appeared, was a return to the UFC.
Not according to White, however.
"That fight might not even happen," White told reporters Friday before ceremonial weigh-ins for UFC 236. "We haven't even talked to Brock. I don't know if he'll fight again, but we don't have a date right now. When Brock Lesnar is ready, he'll call me."
Lesnar (5-3-1) previously fought in the UFC, claiming the heavyweight title after defeating Randy Couture by second-round TKO in 2008. He went 2-2-1 following the win before retiring from MMA and rejoining the WWE.
Cormier has not fought since defending his belt against Derrick Lewis at Madison Square Garden in November. He has not lost since a unanimous-decision defeat to Jon Jones at UFC 182 in 2015. He was knocked out by Jones at UFC 214 in July 2017, but that result was changed to a "no contest" after Jones tested positive for turinabol, an anabolic steroid.
White said that if the Lesnar fight does not come together, Cormier is likely to face former UFC heavyweight champion Stipe Miocic.
Cormier knocked Miocic out at UFC 226 last July.
"The first fight might be Stipe," White said. "We got to wait for Cormier. He went back to the gym, I think, two weeks ago and did a light workout. He's still not healthy. As soon as he's healthy to fight, we can make a decision on when we'll do him and Stipe."