"The president is not going to apologize. Are you kidding me?" Cuban said on CNBC.
"Instead of getting on his phone and tweeting, just read a book. You know, just chill," the owner of the NBA's Dallas Mavericks added in a "Squawk on the Street" interview. "I know that's crazy to say about our president."
High-profile sports figures said Trump should apologize for calling protesting NFL players "son of a bitch" at a rally in Alabama on Friday.
In the interview Monday, Cuban said Trump should have said nothing about NFL players protesting during the national anthem. He also said the league has always been involved in politics at some level.
Cuban supported Democrat Hillary Clinton in the 2016 presidential election. Cuban has criticized Trump over issues and Trump has blasted Cuban likewise.
The uproar started when then-San Francisco 49ers quarterback Colin Kaepernick kneeled during the national anthem last season to protest the treatment of African-Americans in the United States. He is no longer in the NFL.