Jones, in an interview with ESPN's Ariel Helwani, said he doesn't care to set up a third fight with Cormier, the current lightweight and heavyweight champion whom Jones already has beaten twice: by unanimous decision at UFC 182 in 2015 and by knockout at UFC 214 in 2017, though the latter victory was later ruled a no-contest due to a failed drug test.
"I already have all the marbles when it comes to Daniel Cormier," Jones told Helwani. "I've beaten him twice. This game has never been personal. What is personal to me is chasing greatness, not individuals. So in the case of myself and Daniel Cormier, he needs to fight myself one more time if he ever wants to be considered one of the all-time greats. I don't need to fight him again to be considered one of the all-time greats. I have many more years to prove it."
Last week, Jones was given a 15-month suspension by the United States Anti-Doping Agency, retroactive to July 28, 2017, for testing positive for metabolites of an anabolic steroid. He is eligible to return to competition by Oct. 28.
Jones and Cormier exchanged heated words on social media in the days following USADA's announcement of the suspension. Jones threatened to "bury" Cormier in a third meeting; Cormier called Jones a "cheater and a snitch." Cormier also has been critical of USADA for handing out what he deemed a "joke of a punishment" to Jones.
Jones told Helwani that he doesn't think Cormier's criticism is warranted.
"I think this is just another way for him to blame something for him getting knocked out in our last fight," Jones said. "At the end of the day, the way it was described to me, the amount of steroids that were found in my body was the equivalent of throwing a pinch of salt in an Olympic-size swimming pool. There was so little of it in my body, there's no scientific way possible that this could have affected my performance. There's no reason for him to be mad at USADA. USADA didn't get him knocked out."
For Jones' return bout, UFC president Dana White told ESPN last week that the promotion is hoping to set up a fight with Alexander Gustafsson at UFC 232 on Dec. 29 at T-Mobile Arena in Las Vegas.
Cormier, meanwhile, is expected to make the first defense of his heavyweight title against Brock Lesnar. He told Helwani on Monday that he hoped the Lesnar fight would happen in January.
Cormier also told Helwani that he hoped to close out his career with a third fight with Jones, insisting he cannot leave the sport without fighting Jones one more time.
"I can't turn this off," he told Helwani on Monday. "It's what makes me uniquely me: my competitiveness and my desire to fight and compete against the best in the world."
Regarding a possible fight with Cormier for the heavyweight title, Jones told Helwani on Thursday that he is "not really" interested in that either.
"Challenging Daniel Cormier for the heavyweight championship would be me making it personal, and it's not personal," Jones said. "I'm not the one who went home crying the first and second times we fought. That was him. There's nothing inside of me that wants to take things from him or make his life harder in any way. I just want what's rightfully mine. He can have what's rightfully his, and we can all get along."