Lukaku is on a season-long loan deal at Goodison Park from Chelsea, and the Belgian international striker has said that he would like his temporary team to out-perform his parent club.
The 20-year-old told Nieuwsblad: "I hope that my goals will help Everton finish higher than Chelsea. I am at Everton for the season, and I want to do as well as I possibly can for them.
"I also hope that Jose Mourinho and I are both at Chelsea for a long time because I want the best for Chelsea and I know that he is a good manager."
The former Anderlecht frontman has scored four goals in four games this season.