The Belgian striker has been unstoppable for club and country after his £90m summer switch from Everton.
He has 14 goals in 11 games for United and Belgium.
But as he prepares for today’s clash with bottom side Crystal Palace and two more World Cup qualifiers next week, Lukaku can forget any hope of having a rest.
Mourinho said: “Look, in here, without Zlatan we cannot rotate the striker, especially because Marcus Rashford is playing also in other positions.
“So until the moment we have Zlatan we cannot think about giving a rest to our number nine, the same way we give in other positions.
“We cannot do that. Belgium is Roberto’s (Martinez) responsibility and it’s his decision to play him or not to play him.”
Mourinho was clearly hinting that he hopes former Everton boss Martinez will consider giving Lukaku a break this week.
Belgium became the first European nation to qualify for next summer’s World Cup at the start of the month and face easy-looking games with Bosnia and Cyprus this week.
But Mourinho was careful not to be seen to be ordering Martinez to rest his ace.
He said: “It’s Roberto’s responsibility. I cannot, professionally speaking, say do this or do that, You know. It’s Roberto’s responsibility.”
The only game Lukaku has not started for the Red Devils was last week’s Carabao Cup stroll over Burton, although he was even on the bench for that.
And while Mourinho may give his star a breather in League Cup ties, there is the real prospect of Lukaku being required to start every game until Ibrahimovic returns.
Mourinho still insists on revealing no details about the veteran striker’s return from knee ligament surgery, although even the most optimistic estimates put it at December.
But Mourinho seems content that the 24-year-old can cope with the arduous work load.
He said: “He works hard, he rests, he has a great professional life outside the football pitch. He has ambitions, he enjoys.”
Another injury victim about whom Mourinho refuses to talk is French international Paul Pogba, although at least the Manchester United manager is now prepared to admit that his hamstring injury will keep him out “long-term.”
Mourinho said: “He’s injured he cannot play tomorrow and it’s not an injury that I can have the hope I have with (Antonio) Valencia or (Phil) Jones.
“I have the hope to see them in training. Long-term injuries I don’t speak about them.
“Ibra, Pogba, Rojo, I don’t think about these players.”
