The Gunners, who failed to qualify for a European competition for the first time in 25 years last season, lost their opening three league games before securing slender 1-0 wins against Norwich City and Burnley.
Arteta recently spoke with Gunners supporters during a Twitter Q&A session, and when the Spaniard was asked the question of where he sees the club in three years' time, Arteta replied: "Wow, a lot – to take the club where it belongs.
"In three years' time [I hope] we are sitting here and we feel so proud about the club that we have, about the connection that we have with every department of the football club, the connection that we have with our fans.
"That we can identify a team, that we can say 'this is an Arsenal team' by the way they play and what they are able to transmit to the world and that everybody is united and that we are an established club that can carry on to have a lot of success – that's how I see the club in the next three years."
Arsenal, who currently sit 13th in the Premier League table, are now preparing for Wednesday night's encounter at home against League One outfit AFC Wimbledon in the EFL Cup, a competition they last won back in 1992-93.