Punk, real name Phillip Brooks, controversially made his mixed martial arts debut at UFC 203 in September 2016.
The former WWE heavyweight champion took on fellow UFC rookie Mickey Gall, who went into the contest as the overwhelming favourite.
The bout went as many expected and saw Gall, a Brazilian jiu-jitsu brown belt, dominate Punk, before submitting him with a first-round rear-naked choke.
Despite being humbled in his pro debut, Punk is still keen on fighting in MMA’s premier organisation.
Speculation of the Chicago native returning to action heated up on Saturday night when he was spotted cornering Paul Felder for his UFC 218 bout with Charles Oliveira.
White poured cold water on such talk immediately after the penultimate pay-per-view event of the year, revealing that he hadn’t spoken to Punk during the card.
“No, he just came out to support his team-mate,” White said when asked if he spoke to Punk at UFC 218.
“I think he wants to fight again, he told me that.
“But we haven’t talked about anything.”
The UFC’s final pay-per-view show of 2017, UFC 219, takes place at the T-Mobile Arena in Las Vegas, Nevada on December 30.