TMZ caught up with White to ask him about earlier comments from Shields, in which she said she would put Nunes to sleep in a boxing match.
When asked about a potential boxing match between the two, he said: "Amanda Nunes has things that she needs to do here [in the UFC] first, but I'm not opposed to it."
He also invited Shields to try her luck at MMA before discussing the possible rematch between Nunes and Chris Cyborg.
White believes Cyborg doesn't want that fight because she is scared of losing again: "I think it's pretty obvious why she wouldn't want that fight. It's a bad fight for her. I think that [Cyborg] is at the point where she's afraid to lose again. Losing again isn't something she's interested in."
Here is a video of the short interview:
Shields previously told TMZ she would knock out Nunes in a boxing match, but her lack of wrestling ability would leave her with no chance in an MMA matchup:
She later took to Twitter to express her admiration for Nunes:
Nunes is the current bantamweight and featherweight champion in the UFC, adding the latter strap to her collection by knocking out Cyborg in the opening round of their UFC 232 meeting.
It was regarded as the biggest women's fight the organisation could make at the time, but the 31-year-old needed little time to dismantle her opponent.
Her impressive resume also includes two wins over Valentina Shevchenko, as well as triumphs over Holly Holm and Ronda Rousey. As a result, the Lioness is firmly in the discussion of the greatest women's fighter in all of combat sports.
What's next for her is unclear. A third fight with Shevchenko could be made, as she has won three in a row and the flyweight title since their last meeting. Other options include Germaine de Randamie—who has won five straight and was stripped of the featherweight title, rather than lose it outright—or the Cyborg rematch.
Shields has dominated the middleweight division since April of this year, when she beat Christina Hammer to unify all the belts. The 24-year-old previously won two Olympic gold medals and currently sports a perfect 9-0 record. Power is not her greatest attribute, as she only has two stoppage wins as a professional.