McGregor (21-4) suffered a fourth-round submission loss to Nurmagomedov (27-0) at UFC 229 last weekend in Las Vegas. A brawl between the two camps immediately ensued, as Nurmagomedov leapt over the Octagon to attack a member of McGregor's corner.
Later that evening, McGregor wrote on social media he is "looking forward to the rematch." White told "First Take" on Monday that McGregor has also brought it up to him directly.
"[Nurmagomedov] has to go before the Nevada commission, and we have to see what's going to happen with Khabib and this whole mess," White said. "But Conor McGregor has already called me, wanting a rematch.
"That's what Conor has asked for. We'll see what happens with Khabib and what's next. Tony Ferguson looked amazing. Those two have been lined up three different times to fight and it hasn't happened. We'll see how things play out."
The Nevada State Athletic Commission has withheld Nurmagomedov's $2 million disclosed purse, pending a full review of what took place after the championship fight on Saturday. According to White, several members of Nurmagomedov's team were arrested but McGregor has declined to press charges.
McGregor also threw punches at members of Nurmagomedov's camp after the fight. The NSAC, however, quickly deemed his actions did not warrant freezing his paycheck.
Nurmagomedov's teammate at American Kickboxing Academy, Luke Rockhold, said on Ariel Helwani's MMA Show on Monday that if the UFC wants Nurmagomedov to fight a rematch, the promotion will have to pay him more than McGregor, who is by far the highest-paid fighter in MMA.
"If you want Khabib," said Rockhold, a former UFC middleweight champion, "he'll want a record-breaking number."
Nurmagomedov faces potential fines, community service and even suspension for his actions on fight night. White said the UFC will allow the NSAC to conduct its hearings before making a decision on Nurmagomedov's next fight. He also said the UFC took extra precautions to prevent this type of situation, but it was unavoidable.
"We knew some things could happen after this fight, so we had everything in place to make sure that didn't happen," White said. "I didn't see Khabib jumping over the cage like that. He got over that thing quick and was going after one of Conor's cornermen.
"There's no doubt he's justified for being upset, but first of all, you, you just won the fight against the biggest superstar in all of sports, let alone our sport. You just beat him while the whole world was watching. ... The only one getting hurt in this thing now is Khabib. Now he has to go before the Nevada commission."