It is the quickest the club have sold out their season ticket allocation since the capacity of Old Trafford was increased to 76,000 in 2006, according to the Daily Mail.
Adult season tickets at the club cost between £532 and £950 and season ticket holders are automatically allocated and required to buy tickets for home games in FA and League Cup competitions.
The remaining 21,000 tickets for each match go to sponsors, away fans or are sold on an individual basis.
Van Gaal will officially take over as manager at Old Trafford next week after completing duties with Holland at the World Cup.
The Dutchman has been charged with the responsibility of lifting United after a poor last season in which they finished seventh in the Premier League and failed to qualify for Europe.
The former Ajax, Barcelona and Bayern Munich boss underlined his credentials in the past month by guiding Holland to the semi-finals in Brazil.
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