Mourinho left Chelsea on Thursday following a disastrous start to the campaign, with the London club currently occupying 16th position in the Premier League.
Van Gaal insisted Mourinho is a “fantastic manager” and that he was surprised to hear of his departure from Chelsea.
“What can I say? It was a big surprise for me, I didn’t expect it,” van Gaal said.
“He’s a fantastic manager with a record that nobody has in this football world, but it is still possible [to be sacked].
“I have said this, last week or the week before, the main thing is always first, the results, and second, the chemistry between players, manager and his staff.
“I cannot judge what was happening in Chelsea, but I was very surprised [to see Mourinho sacked].”
Van Gaal is under similar pressure at Man United following a string of poor form and there have been calls for Mourinho to replace him at Old Trafford one day.
Mourinho’s reputation has taken a hit this season but the fact remains that he has won trophies at every club he has managed. There may be a stipulation in Mourinho’s contract ruling him out of a job in the near future but United would be wise to at least enquire about his availability if van Gaal continues to struggle at the club.