They met Tuesday at the King Cole Bar at the St. Regis Hotel in New York, according to TMZ, which first reported on the meeting and published a picture of the pair.
Asked whether he could confirm the meeting or give details on what was discussed, Cuban told CNBC that he would "have to pass."
The billionaire entrepreneur and Dallas Mavericks owner endorsed Democrat Hillary Clinton in the presidential election. He repeatedly criticized Trump in appearances on CNBC during the campaign.
Bannon will be Trump's chief strategist in his administration.
It was unclear what Cuban and Bannon would have discussed. Cuban told MSNBC in October that Bannon is "a lot smarter" than Trump, as some of Trump's campaign rhetoric would benefit Breitbart, a right-wing news site in which Bannon was previously chairman.
Disclosure: CNBC owns the exclusive off-network cable rights to "Shark Tank," which features Mark Cuban as a judge.