Cerrone (28-6) extended his division-best winning streak to eight on Saturday, defeating John Makdessi via TKO in the second round at UFC 187.
After the win, White told ESPN.com that Cerrone's next fight will be against dos Anjos, the defending lightweight champion.
"'Cowboy' looked insanely good," White said. "He kept his composure, put together combinations to the legs and head. He looked unbelievable. I will give you this, yes, Cowboy Cerrone is next in line for a title shot."
Cerrone, 32, has been the most active fighter on the UFC roster since 2011 -- but said he's willing to sit on the sidelines and wait for the shot.
"I would love to wait," Cerrone said. "Well, I'll wait for Denver, Colorado. Can I say that? I'll wait for Denver, Colorado.
"I see a lot of 'Sunday Fun-days' in my future. I should be all right."
Makdessi was taken to the hospital Saturday for a suspected broken jaw. Both White and Cerrone praised the Canadian for accepting the fight on short notice after Cerrone's original opponent, Khabib Nurmagomedov, was forced to withdraw.
"I don't want to sound arrogant or cocky but taking a fight on short notice against 'Cowboy,' you have to be mentally strong," Cerrone said. "My hat is off to him for being ready to go and confident. He stood right in the pocket and gave it hell. I hope he heals up quick and we'll see him soon."