Arteta, who completes six years in charge of Arsenal on Saturday, won the FA Cup with the North London club in 2020 but has yet to taste success in the league, his side finishing runner-up in the last three campaigns.
They are currently two points clear this season and have also reached the quarter-finals of the League Cup.
Asked whether he could see himself extending his stay beyond the end of his contract in 2027, Arteta told reporters on Friday: "Yes, but it’s about today. And a lot of things have to happen in the next few months as well to earn the right.
"I think a manager has to earn the right to be here tomorrow. A lot of things have to happen in the next few months as well to earn the right (for an extension)."
The Spaniard said Arsenal's lack of trophies was not down to substandard performances.
"You look at the performances, all the records that we had that were broken in the history of the club. We still haven't managed to do that (win trophies)," he added.
"That tells you the level we are in, which is a level that the Premier League has never experienced in the past."