McGregor is coming off consecutive defeats to Dustin Poirier and is recovering from a broken leg suffered in his loss to the American last July.
Oliveira, who retained his lightweight title against Poirier last month, has said he is “waiting” for McGregor to return to the octagon and wants to face him in May.
That is despite Justin Gaethje’s status as the No 1 contender for the lightweight title, with the former interim lightweight champion expressing his anger at talk that McGregor could be allowed to skip him in the queue.
McGregor, meanwhile, is ranked ninth in the division but former heavyweight champion Cormier has said he would not be surprised to see the Irishman handed the title shot ahead of Gaethje.
“Honestly, I really do believe that there are different rules in regards to Conor,” Cormier told the Schmo.
“And people might not like it, people may hate it, but if he is healthy and he starts to chirp, Oliveira’s chirping back at him, and if there’s fan interest, I can see a world where it happens [this summer].
“It would make so many people upset, but ultimately it comes down to dollars and cents.”
McGregor’s status as the biggest star in MMA history means he is seemingly never far from a title shot, something Gaethje has admitted he is wary of.
When asked about the prospect of McGregor being Oliveira’s next challenger, Gaethje said: “I’d burn it all down. F*****g burn it down, that’s what I’d do.
“[McGregor] is so irrelevant. He has not won a fight since 2016 in the lightweight division, I’m ranked No1. I saw they updated the rankings, I’m No. 1 now; that feels pretty good.
“My whole life I’ve been working towards this, that’s what’s next. If not, I f*****g burn it down.”