"We're not trading any of those players," Leonsis said in an interview with WTOP radio.
Beal and Wall were said to be available earlier this season, with Porter's name being tossed around in trade rumors more recently. But Wall went down with season-ending heel surgery last month, and his large contract ($170 million over four years) already was deterring most opponents from exploring trades.
Both Beal and Wall have said they want to remain in Washington.
Porter Jr. has been mentioned in rumors involving mostly Western Conference teams, such as the Sacramento Kings and New Orleans Pelicans.
Leonsis later added that general manager Ernie Grunfeld also is safe for the time being, but suggested the Wizards will need to make the playoffs it to stay that way.
"I'm happy if we meet our goals." Leonsis said. "We would have to look at the entire organization whenever we don't meet our goals."
The Wizards (22-29) entered Thursday two games behind the Charlotte Hornets for the East's final playoff spot.
The NBA trade deadline is Feb. 7.