The Gunners are currently fifth in the table, two points behind Everton, who reside in the final Champions League spot.
Despite their European future far from being secured, the North London outfit have a chance of ending their eight-year trophy drought after reaching the FA Cup final following a penalty-shootout win over Wigan Athletic on Saturday.
"I think it's still there for us," The Mirror quotes Arteta as saying. "There's still a long way to go - there's four weeks until the end of the season.
"I believe we can do it, but we need to win all our remaining championship games. If we don't, then I don't think we will do it. It's about confidence and it builds a bit of enthusiasm."
Arsenal will take on West Ham United at the Emirates on Tuesday evening.