The 27-year-old midfielder has been out of action since rupturing his cruciate ligament in February and is unlikely to return until the New Year after a fresh setback.
The former Rangers star has been spending time in his homeland as he recovers from his injury and has been linked with a move to Atletico Madrid.
Sticking with the Toffees: Arteta feels at home at Goodison Park
He said: 'I can see myself finishing my career at Everton. That would not surprise me at all. I have never spent as much time at a club as I have spent at here, so that means something.
'I have found a place where I am confident I can achieve my ambitions and where I have improved as a player and learned a lot of things as a person.'
However the latest setback has left Arteta frustrated.
'There was no explanation for the infection, they have had three cases like that in 35 years,' he told evertonTV.
'The surgeon and the medical staff at the club do not want to talk about time, because there is no point. The only worry is to get my knee fixed properly.
'There is no point risking it. I have had three operations and need to take it carefully.'
Without Arteta's influence, Everton have struggled for consistency but he believes there is a lot of quality in the squad.
Arteta added: 'I would like to win a trophy and we have got the potential to do it. We have players who are really involved in the club and players who really love the club.
'I have been at other clubs and this is a special one. People say we are a family - and we really are.
'Maybe people do not realise sometimes how the club works on the inside but we have got really good people.'
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