The Portuguese coach was brought to Spain from Inter Milan after winning the European Cup last May, with success in Europe's elite club competition top of his list of priorities.
Unbeaten so far this season, Real have two wins from two to top Champions League Group G and can all but seal a place in the last 16 with a victory over Milan.
In La Liga, their 4-1 hammering of Malaga on Saturday left them top having scored more goals (16) and conceded fewer (3) than any other side.
"After seven league matches and without much time to work and improve, I am happy with the evolution and with the qualities the team are showing," Mourinho told reporters in Malaga.
"We defend quite well, we are compact, we have good ball possession. We probably have percentages of ball possession that my teams have never had before and we score goals."
After a goal-shy start to the campaign, Cristiano Ronaldo, Angel Di Maria, Mesut Ozil and Gonzalo Higuain finally clicked in front of goal with a 6-1 demolition of Deportivo La Coruna and the convincing Malaga win.
Despite all that, Spain goalkeeper Iker Casillas warned that a showdown with the Italian giants was a completely different matter.
"Madrid v Milan is a classic European encounter. All rivals are tough but this is perhaps our first big test of the year," Real's captain told reporters.
INJURY DOUBTS
Milan have a win and a draw from their first two group games but travel to Madrid after a 3-1 win at home to Chievo that left them vying for the top spot in Serie A with Inter and Lazio.
They have injury doubts over centre back Thiago Silva, courted by Real in the close season, after the Brazilian suffered an ankle injury on Saturday.
Goalkeeper Christian Abbiati also suffered a knock in the game but is expected to be fit while captain Massimo Ambrosini is still out.
Milan coach Massimiliano Allegri, a former Cagliari boss largely unheard of outside Italy when he was appointed in the close season, is relishing the big game.
"You prepare completely separately for a match like the one against Madrid. We will be ready for Tuesday," he told reporters.
"For Thiago we'll see, but if he can't make it whoever goes on the field will do well all the same."
Brazil's Alexandre Pato, who scored twice at the Bernabeu in a 3-2 Champions League win last season, scored another brace against Chievo on Saturday.
He was set up both times by strike partner Zlatan Ibrahimovic, before giving way for former Real winger Robinho to register his first Milan goal near the end.
Teams (probable):
Real Madrid: 1-Iker Casillas; 4-Sergio Ramos, 2-Ricardo Carvalho, 3-Pepe, 12-Marcelo; 14-Xabi Alonso, 24-Sami Khedira; 7-Cristiano Ronaldo, 23-Mesut Ozil, 22-Angel Di Maria; 20-Gonzalo Higuain
