The bout will be for the UFC Lightweight Championship. Nurmagomedov is the reigning champion, while Gaethje is the interim UFC Lightweight champion after beating Tony Ferguson at UFC 249 in May.
Provided the fight goes ahead in October, it will mark Khabib's first bout in more than a year after he last competed at UFC 242 in September. He beat Dustin Poirier by third-round submission to improve to 28-0 professionally.
Nurmagomedov was originally scheduled to defend the UFC Lightweight title against Ferguson at UFC 249, but the coronavirus pandemic prevented him from traveling, which gave Gaethje the opportunity to vault to the front of the line.
Nurmagomedov has not spoken publicly in some time, and he is grieving the loss of his father and trainer, Abdulmanap Nurmagomedov, who died earlier this month from COVID-19-related complications.
White said Tuesday that Abdulmanap's death has been "very rough" on Khabib.
It isn't yet known where UFC 255 will be held, but it could take place in Las Vegas, which is where most of UFC's upcoming events are tentatively scheduled.
If Nurmagomedov beats the 22-2 Gaethje, it will improve his career record to 29-0 and put him one win away from achieving his stated goal of going 30-0.
Per ESPN's Brett Okamoto, Nurmagomedov's manager, Ali Abdelaziz, has said the fighter's plan is to go 30-0 and then retire. White told Okamoto on Monday that he would be open to letting Khabib choose his final opponent if that is the case.
White even left the door open for retired UFC legend Georges St-Pierre to be Nurmagomedov's final opponent since he and his late father had a great deal of respect for GSP.