The Belgium international, back from his loan at West Brom, scored on the stroke of half-time in a 4-1 win against a Malaysia XI in Kuala Lumpur which was effectively their national team.
His strike followed the winning penalty against Bangkok four days earlier and with Mourinho switching his entire side at half-time in pre-season games so far, it means he is averaging a goal every 45 minutes.
“Of course Lukaku can challenge Torres,” Mourinho said. “He is 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 Clarke, 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.”
Mourinho is quick to knock back anybody who is getting carried away with Lukaku’s strong start, however, and dismissed suggestions that Lukaku could be compared to Didier Drogba.
“We have to respect Didier because he is unique in Chelsea’s history, and we have to respect Lukaku,” he said.
“The best way to do that is not to 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.”
His willingness to learn at least gives Lukaku a chance.
Mourinho has already spoken on tour of his belief that Torres struggles to perform against tight defences and is only effective against certain types of opposition.