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Silva was initially named the winner by unanimous decision in Diaz's last fight, but the result was later overturned as 'no contest' after a failed drugs test.
Diaz was in attendance at UFC 261 on Saturday at the VyStar Veterans Memorial Arena in Jacksonville, Florida.
Speaking at his UFC 261 press conference, White confirmed that he would be holding talks with the Stockton-based star about his sensational return to the octagon.
The 51-year-old UFC chief said: "Nick wants to fight. Sure, [we'll give him one]. We'll see how this goes.
"He's waiting for me in the back right now. I'm going to go talk to him."
Who do you want to see Nick Diaz fight on his return to the UFC? pic.twitter.com/42XksXcmgD- UFC on BT Sport (@btsportufc) April 25, 2021
Chimaev, who is undefeated in his nine-fight professional MMA career, could also be Diaz's next opponent as White hinted that the clash could happen.
When asked if it would be too crazy to think of Chimaev being Diaz's first opponent, White simply responded: "No."
Chimaev fought three times in the UFC in 2020, with his last victory coming in a sensational first-round KO demolition of Gerald Meerschaert at UFC Fight Night 178 last September.
The 26-year-old MMA fighter was scheduled to face Leon Edwards at UFC Fight Night 183 last December, but he later pulled out after testing positive for COVID-19.
Chimaev shocked the MMA world by initially announcing his retirement from MMA in March due to complications caused by COVID-19.
However, White has since dismissed that the Russian-born Swedish star has retired by saying that Chimaev was "super emotional" when he made his retirement post on social media.
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