"It's the fight I want," he said. "I think everyone wants to fight Brock. We all want to fight Brock."
He added: "Dana get on the phone right now. If you haven't called him yet, do it today! What are you waiting for? Get this s--t on the books. Let's get this on the books!"
Per MMA reporter Damon Martin, White has previously said he wants to arrange it:
On Sunday, Lesnar lost to Seth Rollins at WrestleMania, and Martin believes that could allow him to make his UFC comeback:
Cormier enjoyed watching his defeat:
Per TMZ, he also urged the 41-year-old to "lick those wounds...'cause I got some brand new ones waiting for ya."
Lesnar, who held UFC's heavyweight championship belt between 2008 and 2010, has not fought since he beat Mark Hunt via unanimous decision in 2016, a result that was overturned to a no contest after he failed a drugs test.
DC talked up his next potential opponent: "It's the fight. That's the fight that needs to happen. You know, he's a former UFC champ, All-American in college. This guy's very, very deserving of a fight, and he's gonna get it. Hopefully."
Cormier (22-1) held the heavyweight and light heavyweight belts simultaneously until he relinquished the latter in December.
He had last defended it in January 2018 against Volkan Oezdemir before winning the heavyweight title from Stipe Miocic in July and defending that against Derrick Lewis in November.
Cormier was named UFC's Fighter of the Year for his efforts:
As for Lesnar (5-3), Hunt was his only fight since 2011. He lost his previous two bouts in the Octagon against Alistair Overeem and Cain Velasquez.
It's difficult to imagine him beating Cormier, but the pair facing off could be a lucrative spectacle.