First off, Amanda Nunes is the greatest female UFC fighter of all time -- with devastating victories over everyone from Ronda Rousey to Cris Cyborg and Holly Holm.

Claressa is the top dog in boxing -- she's 9-0 as a pro and a 2-time Olympic gold medalist.

Shields has made it abundantly clear she wants Nunes in a boxing match -- and told TMZ Sports bluntly, "I'd put [her] to sleep."

So, we asked Dana if he'd ever let Amanda follow in Conor McGregor's footsteps and take a super fight in the boxing ring ... and his answer was VERY interesting.

"Amanda Nunes has things that she needs to do here [in the UFC] first, but I'm not opposed to it," White said.

"Maybe Claressa comes over here and fight in MMA."

So, what does Amanda need to do in the Octagon before a possible Shields matchup?

Dana says he's trying to sign Cris Cyborg to take a rematch with Amanda -- but White claims Cyborg won't put pen to paper ... insinuating she's scared of getting beaten up 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."

White says Amanda Nunes REALLY wants the fight -- and since she's basically cleared out the women's division, White wants to give her whoever she wants.