The Blues take on leaders Leicester City this weekend.
The Blues are currently 10th in the Premier League table and six points behind Manchester United, who currently occupy fourth spot.
They had started the season well but have struggled to pick up the points in recent weeks, drawing their last three games.
With the Premier League very much an open league this season though, Lukaku insists that they can make it into the Champions League this season.
"We want to do well in the League Cup and FA Cup but the Champions League spot is the main goal," he told BBC Sport.
"It is very realistic when you see the results in the league."
"The teams that you don't expect to be up there are getting stronger so it is a really exciting time.”
If Everton are to make the Champions League this season, Lukaku will surely be key to their hopes.
The Belgian has seriously upped his game this season, with 15 games in all competitions so far, 12 of which have come in the Premier League.
Leicester’s Jamie Vardy, who last month set a new Premier League record by scoring in 11 consecutive games, has held him off of top spot though, with 15 goals in the league so far.
He and the Foxes sit top of the table and Lukaku says they deserve to be there based on their performances.
"If a team is number one in the league it means they deserve it. They win games, play good football and are very disciplined,” he added.