However, the pair met before United's 0-0 draw at Liverpool on Saturday, with Ziggo Sport's presenter saying: "Before the game, Jose Mourinho comes up to you, shakes your hand and calls you mister, coach, the boss and says if you want to join us before the game or after in the dressing room just come over ... I didn't know what I was witnessing."
Van Gaal replied: "Remarkable, eh? He is basically a very sympathetic guy. He was like that as an assistant but also as an opponent.
"He only lets himself go sometimes in front of the media and, of course, the way I suspect he took over at Manchester and my sacking went is, for me, not very chic [classy]."
United fans chanted their appreciation for Van Gaal after the draw at Liverpool, and he said that was "beautiful."
Van Gaal led United to a top-four finish in his first season and FA Cup success in 2016.