Yet their friendship dated back to McClaren's days as a club boss at Middlesbrough.
So, while McClaren is anxious not to get into the rights and wrongs of Roman Abramovich's decision to axe Mourinho in favour of Avram Grant, he knows the controversial Portuguese coach will leave a big gap in English football.
McClaren said: "Even when I was manager of Middlesbrough I thought he was good for the game.
"I got on well with him there and as England manager I could not have wanted anyone better to work with.
"He invited me in gave access to the players and let me make the decisions on the players.
"He really did support me all the way through.
"I don't want to get into the politics of it, but it is sad to lose someone of that calibre and that character.
"You only have to listen to the Chelsea players to know what kind of manager he was.
"He has done a lot of good for football and for English players as well."