Shaw has been sidelined since suffering a double fracture of his right leg against PSV Eindhoven in the Champions League in September of last year.
The Englishman recently tweeted to suggest that his recovery is going well and van Gaal spoke about Shaw during his pre-match press conference ahead of the game against Crystal Palace on Wednesday.
“He’s very positive, he’s doing great, I cannot deny that so he’s training on the pitch,” van Gaal said.
“But now he’s training with the physiotherapist and he has to train with the football coach and that still hasn’t happened.”
Shaw’s return to the pitch would be a big boost to everyone involved with United but the club’s medical team will be keen not to rush his recovery.
Perhaps a few cameo appearances towards the end of the season would be best for Shaw, as it would motivate him ahead of the next campaign while giving supporters and players a psychological boost inside the stadium.