Lukaku scored for the second time in as many games for Chelsea in their 4-1 win over a Malaysia XI in Kuala Lumpur on Sunday.
With the club chasing Manchester United striker Wayne Rooney, reports suggest Fernando Torres or Demba Ba could make way if Chelsea get their man.
Speaking after the game in Malaysia, Mourinho said Lukaku would definitely challenge Torres for a spot up front but refused to compare him to Drogba, a three-time English Premier League champion and Champions League winner at Chelsea.
Belgium international Lukaku, 20, starred on loan at West Brom last season, scoring 17 league goals.
"We have to respect Didier because he is unique in Chelsea's history and we have to respect Lukaku," Mourinho said.
"The best way to do that is not compare him to a legend in Chelsea's history.
"Leave Didier where he is, at the top of Chelsea's history, and leave Lukaku to work hard. The kid is good.
"(My team) are learning to play the way I want. Every manager has his own ideas. Lukaku had a fantastic manager last season but Steve (Clarke) is Steve, I am me, and West Brom is not Chelsea.
"It's up to the kid but he's open and intelligent to learn the kind of movement we want. The role he played tonight was the right movement.
"We don't want the striker just aiming between the central defenders but making movements, sometimes between the midfield or moving wide."
Burkina Faso international Bertrand Traore, 17, impressed for Chelsea with a goal and an assist but cannot be signed until his 18th birthday as he is in the United Kingdom on a student visa.
Traore, who also performed well against a Singha All-Star XI on Wednesday, may not receive a work permit and would go out on loan.
"We'll have to wait until he becomes 18 to try to get the permit for him to stay in England," Mourinho said.
"If it's not possible we have to let him go on loan somewhere but we have the guarantee that he plays for his national team.
"For a 17-year-old boy, sooner or later, the committee has to give him a permit to play in England.
"If he goes on loan somewhere, he has to go, but if he's playing for his country at the same time, one of the most important countries in African football, he'll get his deserved permit."