White told Pugmire his focus is on determining if McGregor could fight at UFC 219 on Dec. 30 in Las Vegas.
"That's all this week," White said. "We're working on that [main event]. I have to have it done by the end of the week."
McGregor is approaching a year since his last fight in UFC. He beat Eddie Alvarez at UFC 205 on Nov. 12, 2016, to capture the UFC lightweight championship.
The 29-year-old took a brief hiatus from mixed martial arts to train for his boxing match against Floyd Mayweather Jr., who won by TKO in the 10th round.
Pugmire wrote a matchup with Tony Ferguson would make the most sense for McGregor in his first MMA fight back. Ferguson is the No. 1-ranked challenger in UFC's lightweight rankings, and he won the interim lightweight title by beating Kevin Lee at UFC 216 in October.
In an interview with Ireland-based entertainment.ie (h/t MMA Fighting's Shaun Al-Shatti), McGregor expressed an interest in fighting Ferguson without mentioning him by name.
"I know there are many contenders in the UFC," McGregor said. "There are many boxing contenders as well. What interests me is certainly a UFC bout, certainly a defense of my lightweight title. There is a fighter with the interim lightweight belt. I feel that will be next. We'll see how negotiations go."
Regardless of his opponent, UFC will be happy to have McGregor back in MMA after his short-lived transition to boxing. Four of the UFC's five biggest pay-per-view buyrates came with McGregor in the headlining fight.
McGregor is UFC's biggest star, and he's even more valuable to the company with Jon Jones facing a lengthy suspension and Ronda Rousey's MMA career potentially over. His return to the UFC—especially if he's fighting Ferguson—would almost certainly be among the company's highest-grossing events of the year.