The Ivorian striker arrived at Goodison Park at in July after impressing under Roberto Martinez at Wigan Athletic with 11 goals in 34 league appearances.
However, the 30-year-old struggled with knee injuries throughout the season just gone and was only able to make five appearances in the Premier League, with no goals.
Kone has now vowed to show the Everton faithful he can step into the shoes of departing Romelu Lukaku and says he will be working hard over the close-season to be ready for the start of the new campaign.
"The most important thing is for me to be in the best possible shape I can be for the start of next season," he told Everton's official website.
"I look back with a bit of pain (on the season). I have not played as many games as I would have liked due to this injury.
"That is why I am not going on holiday, I am staying in Europe to work hard over the summer period, so I can hit the ground running when pre-season starts in July.
"The plan is to go back to Belgium, to the rehab centre where I have been working, then I will come back to Finch Farm (Everton's training ground) for a fitness check.
"Then I will go back to Belgium but I will be back before the rest of the team to start pre-season."
