The Manchester United manager spoke of his concern at the club's domestic and European schedules following his side's 2-1 victory against the German side at Old Trafford.
"As a manager, you want to prepare on the pitch and you can't do it because you need freshness of the players," he said on Thursday.
"The solution is recovery - recovery, recovery, recovery. That is why it is so difficult to prepare (for) the match against Arsenal."
Arsenal have an extra 24 hours to prepare for Sunday's match at The Emirates stadium, having played their Champions League game against Olympiakos Piraeus on Tuesday.
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Van Gaal said there were no fresh injuries following Wednesday's win at Old Trafford, but he said it would not be until Saturday that he could assess the fitness of his players.
"Another solution is to change your squad," he said. "We'll have to see how the evaluation is of my fatigue specialist.
"I cannot tell (now) because the press conference is one day after the match. Tomorrow they have the day off. We have to wait and see for Saturday, and I can make decisions."
However, the Manchester United boss said Michael Carrick, who missed Wednesday's Champions League game with what Van Gaal called a "minor injury", would be available for selection against Arsenal.
The manager also praised the form of defender Chris Smalling and Ashley Young, who filled in at right-back in the second half against Wolfsburg.
He said of Smalling: "I help him with advice, demands, training sessions and showing images to improve him, but he has to be open (to it) and he has to perform on the pitch.
"He does everything himself. The greatest compliment you have to make to Chris and not to me."
Winger Young was brought on to replace Antonio Valencia at right-back during United's victory over Wolfsburg, and Van Gaal said: "He is very important. He is a team player in the first place.
"Not many players are actually team players but he is always thinking of the team, and he can play in a lot of positions. For a manager, it is fantastic that he is willing to do that."
(Reporting by Neville Dalton)
