"It is going to mean an awful lot to me to wear that shirt next season because I've not made my mark in the club's history," Kone told evertontv. "The season coming for me is where I have to prove my worth and I am ready to take on that challenge."
Kone, 30, followed manager Roberto Martinez to Goodison Park from Wigan Athletic last year in a deal worth around £6m. However, he made just six appearances before sustaining a knee injury in October that ruled him out for the rest of the 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 said. "I have decided not to go on a big 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. This season has been pretty much a non-starter for me so next season is when it starts. It is all about working hard so the fans can see the best of Arouna Kone."
In Kone's absence, Everton finished fifth in the Premier League, earning them a berth in next season's UEFA Europa League.