Shaw broke his right leg in two places during United's 2-1 defeat to PSV Eindhoven on Tuesday.
The 20-year-old had an operation on the night of the game and has stayed in Holland since to continue his recovery.
But Van Gaal said he could return to Manchester on Saturday.
The United manager said: "His family is there, we have sent people with him and he will come back when he is prepared
Maybe tomorrow."
Shaw left the pitch at the Philips Stadion on a stretcher while receiving oxygen following a late tackle by Hector Moreno.
The former Southampton left-back was in tears at the time, but is now in better spirits, according to his manager
"I called him last night," Van Gaal said
"He sounds very strong, which was amazing for me - a big surprise.
"It is a good signal, but he knows he has long way to go and it is not easy..
He will have a long period of rehabilitation (when he is back) and he has a long way to go."
Source : PA
Source: PA