Arsene Wenger's side trail a resurgent City by three points, after a Sergio Aguero hat-trick completed a 6-0 rout at Etihad Stadium today that relegated QPR.
Goal difference could also come into play, with a free-scoring City now eight goals better off than their North London rivals.
Arsenal will expect three points tomorrow night, before City themselves travel to the Liberty Stadium on 17th May to face Swansea, who are heading for their best Premier League season to date under the astute leadership of Garry Monk.
City end their season at home against a Southampton side seemingly desperate to avoid playing in next season's Europa League.
Arsenal, meanwhile, face a tricky-looking home game on Wednesday 20th May, a 7.45pm midweek kick-off, against Dick Advocaat's Sunderland who are scrapping for their Premier League lives.
They end at home to West Brom, whose upturn in form under Tony Pulis means they have long since secured Premier League safety.
Perhaps the main aim for both teams will simply be to finish ahead of Manchester United, who all but guaranteed fourth place at least when Liverpool drew with Chelsea at Stamford Bridge this afternoon.
United trail Arsenal by two points, but like City have played two games more and look odds-on to face a tricky Champions League qualifying tie just prior to the start of next season.
They welcome Arsenal to Old Trafford on Sunday 17th May - a game which could prove crucial in the final shake-up.
The equation, then, is not a difficult one. If Arsenal 'win out', they will finish second. Slip up, and City's supposedly dire season under Manuel Pellegrini will start to look a whole lot better.
Sunday 17th May
Swansea v Man City (1.30pm)
Man Utd v Arsenal (4pm)
Wednesday 20th May
Arsenal v Sunderland (7.45pm)
Sunday 24th May
Arsenal v West Brom (3pm)
Man City v Southampton (3pm)
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