Rooney will be the subject of a third bid from Chelsea after the bank holiday encounter at Old Trafford, when Belgium forward Lukaku aims to start and build on his 17 goals on loan for West Brom last term.
"Every player wants to be in the best team there is," Lukaku said. "If a player can improve us, why not? Samuel Eto'o, Wayne Rooney, I have heard everyone. I am not scared. Let them come."
"I'm getting closer to where I need to be and hopefully also closer to the starting line-up, my main ambition," the 20-year-old former Anderlecht striker added.
"If I keep working hard, like I'm doing now, showing the talent that I have hopefully I get to start in the next game.
"Compared to the first year, when I arrived here it was all about learning and taking a bit off all the players, now it's about starting games."
The physically imposing Lukaku offers a different attacking threat for Chelsea and is often likened to former Blues striker Didier Drogba, who he used to sit next to in the dressing room on his arrival from Belgium.
Mourinho has been wary of the Drogba comparison and Lukaku is too.
"There will always be comparisons but I have my own name," Lukaku said.