The England left-back sustained ligament damage during United's 2-1 win at Arsenal in the Premier League last weekend.
It was reported that Shaw could be sidelined for the rest of the year, but United boss Van Gaal on Friday stated that the teenager has not suffered serious injury.
Van Gaal also confirmed that Marcos Rojo and Radamel Falcao could be included in the squad for Saturday's Premier League encounter with Hull City at Old Trafford.
Argentina defender Rojo has not featured since dislocating his shoulder in the Manchester derby this month, but is on the verge of a return.
On-loan striker Falcao has been back in training this week after recovering from a calf injury and could make his first appearance since coming off the bench in a 2-2 draw at West Brom last month.
Media reports have suggested that Van Gaal is set to drop Robin van Persie to the bench for the game against Steve Bruce's side after just one goal in his last six games for United.
The former Netherlands coach was giving nothing away with regards to his selection in Friday's press conference, but warned that none of his players are guaranteed a starting berth.
He said: "Every player has to fight for his position and I shall always pick the best of the players. It has to be a suitable mix."
Van Gaal also urged his side to be more ruthless as they attempt to ensure they are back in the UEFA Champions League next season.
"We have to improve our playing style and beat opponents more easily," he said.
"We are still fourth so I am happy, but we have to be at least fourth at the end of the season, not now."
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