Cuban said he would consider selecting Griner, a three-time All-American and Big 12 conference player of the year, in the second round of the NBA draft, ESPN reported Wednesday.
If she's not selected, Cuban said he had "no problem whatsoever" inviting Griner to try out for a spot on Dallas' summer league team.
"If she is the best on the board, I will take her," Cuban said Tuesday. "I've thought about it. I've thought about it already. Would I do it? Right now, I'd lean toward yes, just to see if she can do it. You never know unless you give somebody a chance, and it's not like the likelihood of any late-50s draft pick has a good chance of making it."
The 6-foot-8 Griner dominated women's college basketball, scoring 3,283 points and blocking 748 shots in her career. She had 18 dunks, including 11 her senior season that ended abruptly March 31 when Louisville surprised Baylor, 82-81, in the NCAA women's basketball tournament.
Responding to Cuban's comments, Griner posted on her Twitter page, "I would hold my own! Lets do it."
Former UCLA star Ann Meyers tried out for the Indiana Pacers in 1979.