MMA's Kayla Harrison's 'Frenemies' with Ronda Rousey, Gunning for Cyborg?

They were teammates and roommates ... but now MMA rising star Kayla Harrison says she's gunning to take Ronda Rousey's place as the greatest female fighter of all time.

"Ronda always used to call us 'Frenemies,'" Harrison tells TMZ Sports ... "I've always kinda had a chip on my shoulder. Like, anything Ronda could do, I could do better."

"She's always sorta been my motivation behind the scenes."

Kayla trained with Ronda every day for 7 years back when they were coming up in the judo world together ... but says they're very different people.

Harrison won 2 gold medals in her Olympic judo career -- one in 2012 and another in 2016. Now, the 28-year-old is focused on destroying people in MMA.

"I want to be the best fighter in the world. I want to go down in history as one of the most dominant female combat athletes there ever was."

Kayla is 2-0 as a pro MMA fighter, and takes on Moriel Charneski at the PFL 2018 World Championship on New Year's Eve at Madison Square Garden.

As for her next opponent, Kayla's manager Ali Abdelaziz says he's got his sights set on Cris Cyborg.