Rousey is scheduled to fight Liz Carmouche at UFC 157 on Feb. 23, but McMann may be next in line for a title shot.
"I think probably the most interesting matchup would be me and Sara McMann," Rousey told Yahoo! Sports. "[McMann] is an Olympic medalist wrestler who has about the same record as I do right now. She is undefeated and I think she asked for another fight to prepare before she fights me. So yeah, I'm looking forward to fighting her and I think it would be great to have two female Olympic medalists in two different grappling arts fighting each other. It brings a level of credibility to the female fighters."
"There are grinders," White said of fighters in the UFC. "We got guys like Roy Nelson who say that all that matters is winning; doesn't matter how you win, just as long as you win. [But] I would say me and 90% of the fight community like people who are finishers."
Rousey hasn't yet fought in the UFC, but White makes a good point.
Rousey, 25, finished all nine of the MMA bouts she competed in. She has never let a fight go past the first round, as she won via armbar in all nine of her MMA appearances.
"We were just talking before this interview about who? Mike Tyson. Why did everybody like Mike Tyson? Because he had fantastic boxing skills and loved to go the distance? No, because when you watched a Mike Tyson fight, you knew somebody was about to be executed," White said. "When Tyson would walk into an arena you would get goose bumps. As a fight fan those are the kind of fighters you like. And trust me when I tell you, Ronda Rousey is that person."