Fired by the 19 goals of the in-form Dutchman, Arsene Wenger's side have recorded seven wins from the last eight league games ahead of Sunday's trip to the Etihad Stadium.
The north London side have quickly climbed back to within striking distance of the top four following an appalling start to the campaign - and inflicting a second straight defeat on the high-flying Blues would reduce the gap on the summit down to just six points, although Manchester United could overtake their rivals if they win at QPR earlier in the day.
Van Persie - who has smashed 33 goals in 2011 - believes Arsenal must always aim for the top."We should have higher expectations every week, but for now because we have only played 15 games in the league we are not even halfway," Van Persie told Arsenal Player.
"I don't think it's clever to be excited by fourth, fifth, sixth or whatever. We still have to play many games.
"So many things can happen - you see that Spurs lost three points last week, Chelsea beat Manchester City.
"It is an open league and anything can happen. Lots of stuff will happen that is surprising so we have to make sure that we are on the good side and actually surprise people with our results."
Van Persie feels Arsenal have turned their season around through sheer hard work following a humiliating 8-2 defeat at Manchester United on August 28.
The Gunners skipper added: "Everybody had written us off to come back from something like that and weren't speaking positively about us.
"To bounce back from a period like that you can say that everybody earns some credit because we had to dig deep - trust me."
Arsenal showed their new-found resilience when they won 5-3 at Chelsea - where City lost 2-1 last Monday night.
Van Persie is looking forward to another challenge on Sunday.
"It's going to be a big test but we have played against world-class sides before - nobody really expected us to beat Chelsea 5-3 away, but we did it," he said.
"I don't see why we can't surprise again. We're having a good run. Everybody is confident and believes in themselves. The spirit is as high as it can get."
The Dutchman, however, is expecting a tough contest from City's wounded squad, who failed to qualify for the knockout stages of the Champions League before then going down at Stamford Bridge despite taking an early lead.
"Normally, good teams bounce back. You never really know," Van Persie said.
"I remember playing Manchester United a couple of years ago after the unbeaten season when we lost our first game 2-0 at Old Trafford. The following four or five games we didn't win somehow - it was always a draw and somehow we couldn't win.
"That was our bit of history but you never know how they will pick it up.
"Hopefully we can get a good result and everybody is looking forward to it, preparing well.
"This is what you want as a player - you want to play in those games where you don't know what's going to happen. They don't know what will happen either, and that's what makes it interesting."