The England international, 20, sustained the injury in his side's 2-1 Champions League defeat at the hands of PSV on September 15 and has since been working on his recovery.
Van Gaal is reluctant to set a return date for the left-back, yet the Dutchman has revealed the defender is on schedule with his recovery.
"Luke is progressing well and is doing as well as we could have hoped at this stage," Van Gaal told the official United matchday programme.
"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 joined United from Southampton ahead of the 2014-15 campaign, but struggled to live up to the high expectations in his first season at Old Trafford.
He impressed in the opening weeks of this campaign, though, before suffering the serious injury in Eindhoven.
