Cuban told reporters before Tuesday night's game between the Mavericks and the Lakers that if Griner is the best player available, "I will take her."
The 6-foot-8 Griner finished her college career as the NCAA leader in blocked shots and the second-leading scorer in women's college basketball history.
Cuban says he has already thought about it and "Right now, I'd lean towards yes, just to see if she can do it. You never know unless you give somebody a chance."
Cuban said Griner would have to make the team and he isn't "opposed to giving her the opportunity."
He adds: "That'd sell out a few games."
Griner responded with a tweet: "I would hold my own! Lets do it"
Ann Meyers Drysdale was the first woman to get a tryout with an NBA team. The former UCLA and U.S. women's Olympic team star signed a contract with the Indiana Pacers in 1979 but didn't make the team.