The Chelsea coach revealed his admiration for the Germany forward but stressed that he will need to prove himself against more robust defences than Portugal's in the tournament
The Bayern Munich attacker scored a hat-trick and Mats Hummels added another as Joachim Low's side secured a comfortable victory in their Group G opener after Pepe was sent off following an altercation with Muller.
The striker was top-scorer in the 2010 World Cup in South Africa and his three against the Selecao took him to eight goals in seven World Cup finals appearances - though Mourinho suggested he found it too easy in Salvador.
"I would like to see Muller up against a compact defence," the 51-year-old told Yahoo Eurosport.
"That would test him. Portugal were far too weak. There are plenty of teams at this World Cup who defend far better, are much tighter and better organised."
Mourinho did, however, take the time to praise Muller, who scored 13 times in the Bundesliga last season, for his ability in front of goal whilst stressing that his national side were lacking in that part of the pitch.
"He's incredibly dynamic and has a unique goalscoring instinct," he continued.
"He finds room on the field that nobody else knows about. But I still think that, even with Muller, Germany don't have a real forward in their team."
Germany play Ghana on Saturday in their next Group G game.