The Belgian striker performed brilliantly on loan with West Bromwich Albion last season and has franked that form with two goals in two matches in the Blues' pre-season tour of Asia.
However, Mourinho feels the public and media mustn't liken Lukaku to Drogba because he is simply his own man.
"We must respect Romelu and not compare him with Drogba as Drogba is a legend in this club," he said.
"I am happy with his movement and he did what we asked of him. Steve Clarke did well with him at West Brom last year."