The play-off will only take place if results on Sunday mean the two London clubs are equal on points, goal difference and goals scored.
A Premier League statement said: "Should a play-off be necessary the Premier League has made arrangements for a single match to take place at Villa Park on Sunday 26 May 2013. The match will take place early afternoon with a kick-off time to be confirmed should results require the match to go ahead."
Chelsea are due to play City twice in the USA - with the second match at New York's Yankee stadium on May 25, the day before the play-off date. The Premier League statement says both the clubs have been consulted.
It states: "In the event of results in the Chelsea v Everton and Newcastle v Arsenal Barclays Premier League matches being a Chelsea draw, and an Arsenal win by a single-goal margin having scored two more than Chelsea, both teams would be level on points, goal difference and goals scored."
Under Premier League Rules this would lead to a play-off being required to decide which club finishes third and fourth, thereby determining which club enters the UEFA Champions League at the group stage and which at the play-off stage.
Tickets will be allocated equally between each club and will be priced at £20 and £30 with concessions for children and senior citizens priced at a 50% reduction.
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