Shaw suffered a horrific double leg break during the Champions League encounter against PSV Eindhoven a few months ago and it was believed at the time that the left-back would be out for at least a year.
Recently, Shaw has shown signs of a quicker than anticipated recovery by making a return to the gymnasium but despite the good progress, van Gaal has revealed that the club are not looking to rush things and the England international will know more about his progress by Friday.
Van Gaal said: "You have to be very cautious I think because you know with an injury like that it can be going very well but one week it can be going very bad and then he is months behind the schedule so you cannot say that.
"You can only say how he is dealing with his injury and I think that is very good. But at the moment he is a little bit fed up with the daily routine so I give him also four days off, also because it is PSV we are playing. I thought why is he fed up? Maybe it is also because of the match of PSV. But Friday he has a scan and we do then more about the injury how it is going."