Wittman's comments come after Wall, who has five non-displaced fractures in his left hand and wrist, came out of Game 5 on Wednesday without any swelling or other problems.
However, Wittman revealed that Wall will be checked by the team's medical staff as a precautionary measure.
"He'll get checked again later with our doctors," Wittman said during his press conference on Thursday. "Just to make sure everything is where it is supposed to be. After the game, everything looked good in terms of no swelling. That was a good sign.
"Right now I am anticipating that he will be able to play [in Game 6]."
Wall, who injured his hand and wrist in Game 1 on May 3, finished with 15 points, four rebounds, seven assists, four steals and two blocks shots during the Wizards' nail-biting 82-81 loss to the Hawks in Game 5.
Hawks center Al Horford scored the game-winner and gave the Hawks a 3-2 lead in the series with a put-back lay-up with just one second left to play.
While Wittman was gutted about the loss, he was impressed with Wall's performance and admitted that the 24-year-old had exceeded his expectations.
"It was incredible," Wittman said. "Seriously. If you think back to where he was … 10 days ago to where you couldn't tell he had five fingers because it was so swollen to finding five fractures to playing the game that he played.
"He's the toughest kid I have been around. I think that was evidenced last night, to come back from the injury that he has and to really not just try to play but play the way John plays with reckless abandon."