The Wizards reached the playoffs for the first time in six seasons in 2014 during their second term under Wittman's coaching.
NBA.com reports that the former shooting guard is expected to be handed a three-year deal worth $3m (£1.8m) per year.
Meanwhile, team owner Ted Leonsis told NBC: "I thought the coach did a very fine job for us. We're sitting down and talking to Randy and his people. Randy did a very fine job.
"The players respected the coach, and they played hard for him. I think he deserves the opportunity to come back and lead us even deeper in the playoffs."
Wittman was named as the head coach in 2012 after three years as an assistant with the team.