Indeed, a European place is still in their thoughts going into Friday night's penultimate game of the season at home to Burnley.
Keane told the Mirror: "That's the next step.
“For five or six years now, Everton have been around the top six, been top of the pile of the clubs behind the top six and had the odd season in the top six. But we need to try and push on as a club and I'm sure the owners have that in their mind as well.
“It's really exciting times with the new stadium as well, which is a while away but it's in the pipeline.
“We need to make the next step as a team. It doesn't happen overnight and we need to come together next season, take it one step at a time and see where it takes us. It's something we want, we want to take the next step and be in Europe."