Shaw fractured his right leg in two places following a tackle by Hector Moreno in United’s 2-1 defeat at PSV Eindhoven seven weeks ago.
Van Gaal claimed after the match that Shaw could be playing again in six months, but the United manager is now reluctant to pencil in a return date for the 20-year-old.
“Luke is progressing well and is doing as well as we could have hoped at this stage,” Van Gaal wrote in his programme notes ahead of Tuesday’s Champions League match against CSKA Moscow.
“We are not putting any timings on his recovery or a return, as it is important we allow nature to take its course.
“Luke is working hard during his recuperation to keep his body in the best possible condition.
“He is receiving plenty of messages of encouragement from supporters, which I know he appreciates.”
Shaw endured a difficult first season at Old Trafford following his £30million move from Southampton, but started his second campaign at the club in fine form.
England manager Roy Hodgson has not ruled out taking the defender to the European Championship if he makes a full recovery by next spring.