Mourinho signed the winger during his first stint in charge of Chelsea in 2004 as a 20-year-old and he has since gone on to play for Real Madrid and Bayern Munich.
Now at the age of 30, Mourinho believes that Robben has shown this summer that he has developed into a leader.
"Robben is a big player, he is not a kid anymore. He is thirty years old, it is probably his last World Cup in the maximum of his potential and Robben is showing everything he has showed during his career, the quality he has," he told Yahoo.
"At the same time he is showing a physical condition and mental condition that we have to say is really amazing and I'm happy for him because he's a very good guy. He is fighting in an unbelievable way and leading his team, and for me this is fantastic, this is absolutely fantastic."
Robben is expected to be a part of the Dutch starting lineup for tomorrow's semi-final against Argentina.