Davis, 28, earned a third-round submission victory over Baszler on Jan. 5 at Invicta FC 4, which evened their ledger at one apiece.
In 2010, Baszler defeated Davis at the Freestyle Cage Fighting 40 event in Oklahoma, so a rubber match would settle the score once and for all.
"She was just saying at least we'll have a rubber match, so who knows," Davis said following her win over Baszler at Invicta FC 4. "I would love to fight her again."
Davis isn't sure if her victory puts her in line for a UFC title shot against the winner of Ronda Rousey vs Liz Carmouche, or if it will lead to an Invicta FC bantamweight title fight.
"I have no idea what's going to go on right now," Davis said after defeating Baszler. "Your guess is as good as mine. We'll see what happens."
In all likelihood, Davis and Baszler will meet again sometime down the road. Both women are still legitimate top five bantamweight contenders, and close to their fighting primes. Their first two fights were both exciting and evenly matched, so why not complete the trilogy?
"I always have so much respect for Shayna," Davis said. "She's one of the top submission fighters in the game, regardless of what weight class. My gameplan was to try to keep at a distance. I knew she was going to come in with a lot of jabs, a lot of jab-cross. I was trying to play off of that and attack the legs."
Davis is one of the most exciting strikers in female MMA, but her patient, tactical approach at Invicta FC 4, led to her hand getting raised at the end of the tilt.
"She's tough and hard to tap," Davis noted. "I'm notorious for go, go, go and get caught. I knew that was going to be part of her gameplan, so I was trying to be patient more than anything and then wait for the opportune moment."
No word yet from Invicta FC who Davis or Baszler will fight next.