When asked on Monday whether he'd given more thought to the issue, the owner of the Dallas Mavericks and co-host of "Shark Tank" told The New York Times in an email "Yes. But not willing to discuss at this point."
Cuban, an outspoken critic of Trump, has previously said his decision hinges on whether his wife and family would allow it.
I would run as a "Republican before Democrat and most likely independent," Cuban said at The New York Times DealBook Conference in November.
"I think there is an incremental value for setting up an independent candidacy," he added at the time. "The benefit of being an independent is you go right to the golden ticket time, if I get enough support in the polls then I get to participate in the debates."
Cuban's latest comment comes amid growing speculation that a number of familiar business faces could make a bid for the White House in 2020.
A longtime supporter of former President Barack Obama and Hillary Clinton during her bid for president, Schultz told employees in a memo that he's considering several paths forward, including philanthropy and public service.
In an interview Tuesday on CBC's "Squawk Box," Schultz said: "There's a lot of things I can do as a private citizen other than run for the presidency of the United States."
"Let's just see what happens," he added.
Disclosure: CNBC owns the exclusive off-network cable rights to "Shark Tank," which features Mark Cuban as a panelist.