The 27-year-old has been linked with a return to his native Spain.
He said: “You never know how long you are going to be with a club, but I can see myself ending my career at Everton.
“I’ve been at other clubs and I’m telling you this is a special one. The papers say, ‘Mikel wants to go back to Spain soon’. That is not true, I never said that.
“They say would you like to come one day, probably I would like that but maybe I am going to stay for another seven years. I would like to win a trophy with the club. We have got the potential to do it.”
Arteta has been out with a cruciate ligament injury since February, but insists he will not rush a return from the injury.
The Spaniard is not expected to feature for the Toffees until the new year.
“It has been a hard period for me but sometimes you can avoid problems and sometimes you have to take it the way it comes,” added Arteta. “There was no explanation for the infection. They have had three cases like that in 35 years and the surgeon does thousands of operations a year.
“The surgeon and the medical staff at the club don’t want to talk about time, because there is no point.
“The only worry is to get my knee fixed properly and to get it fixed for the next seven or eight years of my career. That is my only aim.
“I want to be playing as soon as possible; but only as soon as my knee says I am ready to do it, because there is no point risking it. I have had three operations and I need to take it carefully.”