The Toffees are seventh in the Premier League and sit eight points behind Manchester City, who occupy the fourth and final Champions League spot having played a game less.
Lukaku, 23, has been integral to Everton’s promising campaign and is top of the goal charts with 21 in 29 matches.
The Goodison Park side are intent on keeping the Belgium international, but he has suggested he could leave in the near future in search of silverware.
In the meantime, though, he wants to end the season on a high.
“I want to create history at the club,” Lukaku, speaking to EASPORTS.com, said. “I want to push for a top four spot and I think we have to aim for this.
“Personally, I just want to improve and become a better player than I am today.
“The season isn’t over yet and we want to do even better than we are already doing.”
Although the former Chelsea player was criticised for his performance in Saturday's 3-1 loss to Liverpool, he had scored five goals in the four games prior. That form, he says, is the result of his intense training.
“Hard work, continuous hard work and dedication," he said when asked what the source of his efficiency is. "I give my best every day in training and in games; this is the only way that I know how to play football.
"I always want to win and that’s the same with my team-mates. At the moment, we are doing really well and we need to continue like this.
“Physically we’ve been working really hard this year and I feel my fitness levels have been improving throughout the year. I ensure I am focused throughout the game whether that is making a chance for myself or receiving the ball from a teammate to score.
“I think I’ve proven that I’ve improved every part of my game. I have always been scoring goals and now the quality of goals I am scoring is better. I can now create chances to score for myself, and I have scored a free kick this year too. I have been scoring a lot more headers and my overall finishing has improved a lot.
“My overall play has improved but I want to give a lot more as I go through my journey in football.”
Romelu Lukaku was speaking to EASPORTS.com at the presentation of the EA SPORTS Player Of The Month Award. To read the full interview, click here.