Ibrahimovic signed a one-year contract with United this week, having been sidelined since April.
Ibrahimovic, 35, signed a one-year contract with United this week, having been sidelined since sustaining a serious knee ligament injury four months ago.
Lukaku has made an impressive start to his Old Trafford career, but Mourinho says that when Ibrahimovic returns to fitness, he will be given a chance to take the Belgian's place.
"Zlatan knows me," Mourinho told reporters on Friday. "And he knows that I play the players that I think are the best for the team. I always did it.
"I always did that in my life, so if he comes here and he proves that he is the best, he plays. If the other ones don't give him a chance to prove that, that's life.
"But I try always to be honest with my players and with my team. I try. Maybe sometimes I do not the correct things. But I always try to do."
Lukaku, 24, has made a strong impression following his £75 million ($96.6 million, 81.3 million euros) move from Everton, scoring four goals in his first three United appearances.
While Mourinho envisages Ibrahimovic playing a key role over the second part of the season, he is similarly insistent that the experienced forward will have to force his way into what could be a settled team.
"Zlatan is going to arrive into a made team," said Mourinho ahead of Saturday's home game with Leicester City.
"Zlatan is going to arrive to a team that, I don't say is the end product, but he is going to arrive mid-season with the team playing in a certain way and with players having what I call the functional links in the dynamic of the team.
"So nobody should be worried with Zlatan and I think for you it's just a funny exercise of football brain to try to anticipate what we are going to be when he comes back, but we are going to be a better squad."
He added: "We need a striker and we have one striker just around the corner that belongs to our family, that likes to be with us and play for us.
"Probably in January I would be knocking on (executive vice chairman) Ed Woodward's door asking for a striker for the second part of the season and I don't need to. I have one of the best in the world."