The Dutchman led Netherlands to a third-place finish at the World Cup in Brazil earlier this year, but has struggled since assuming the reins at Old Trafford.
United currently sit seventh in the Premier League having won just four of their opening 11 matches, and Van Gaal admits the nomination took him aback.
"When you see the results of Manchester United it is unbelievable that I'm on the Coach of the Year shortlist," he is quoted as telling MUTV.
Van Gaal is one of 10 managers and coaches shortlisted for the prize, with Carlo Ancelotti, Diego Simeone, Jose Mourinho and Pep Guardiola among the contenders.
The award - to be announced on January 12 - has never been presented to the manager of an English club, although Mourinho triumphed in 2010 after winning a treble of Serie A, the UEFA Champions League and the Coppa Italia with Inter.
