The Argentine centre-back worked under the Dutch boss for one season while they were both at Bayern Munich, but their relationship was a dysfunctional one.
The pair had a high profile falling out in the early stages of the 2010/11 season after van Gaal dropped Demichelis from Bayern's season opener against Wolfsburg.
Demichelis only made five more appearances for the German side after that and van Gaal allowed him to leave for Malaga in January 2011.
Despite his tempestuous relationship with the new United boss it seems that Demichelis holds no harsh feelings from their time together.
Speaking in an interview before Argentina's penalty shootout victory over Holland last night, Demichelis told newspaper Clarin:
"Van Gaal has been the best coach I have had in my career. At that moment (at Bayern), I was irritated, but I always recognised he was the best football-wise, for the concepts he has and how he imposes them on a team.
"He has shown that in this World Cup. But I didn't leave because of him, but because of my own decision.
"He has a real determination in thinking about the team and potential consequences. I learned a lot from van Gaal."
It is unlikely that City fans and current boss Manuel Pellegrini will be too happy to hear their man giving the coach of their closest rivals such high praise.
Since van Gaal, Demichelis has been very briefly coached by Diego Simeone at Atletico Madrid and Manuel Pellegrini at both Malaga and City.