The England left-back suffered a double leg break during the Champions League contest with PSV Eindhoven—which the Red Devils lost 2-1—following an aggressive tackle from Hector Moreno.
The defender underwent an operation in a local hospital in the Netherlands on Tuesday evening, immediately after the game, and is understood to be recovering well.
Shaw was in tears during the match, as he was replaced on a stretcher, receiving oxygen, but has received support from various fellow professionals—including previous coach Mauricio Pochettino—since his injury.
Speaking to talkSPORT on Friday, van Gaal has indicated that Shaw can be expected back in England on Saturday: “His family is there, we have sent people with him and he will come back when he is prepared. Maybe tomorrow.
“I called him last night,” the Dutch coach continued. “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.”
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Shaw’s injury will have hit him particularly hard following his fitness misfortune last term, when he managed only 16 EPL outings.
He is likely to be out of action for at least six months for United, while his participation for England in next summer’s European Championships is also in doubt.