Liverpool have 73 points with one game left; Man City have 72 with two to play, and Arsenal lag behind on 69 points with two to play.
Champions League qualification would be decided by a play-off at a neutral venue if a combination of the three teams finish level on points with the same goal difference and goals scored.
Eight stars have been nominated for the EA Sports Premier League Player of the Season award, the Premier League announced on Monday.
Even if the Gunners beat Everton on Sunday, they would need Liverpool to draw against Middlesbrough - or Manchester City to lose at Watford with a goal difference swing of five in their favour - if they are to stand any chance of a top-four finish.
The fight will come to an end on Sunday when the fifth placed Arsenal will face Everton in their last game of the season. Liverpool, who have played a game more, are a point above them in third.More news: Senate committee wants Comey to testify
Sanchez scored two late close-range goals to earn Arsenal a 2-0 home victory over relegated Sunderland, while Kevin De Bruyne starred as City comfortably defeated West Brom 3-1 at the Etihad Stadium.
Man City, Liverpool and Arsenal can all still make it in.
The 46-year-old has failed to win the league title only once before in his career - in the 2011/12 season when his Barcelona side finished second in La Liga behind Real Madrid - and before he joined City he won three consecutive Bundesliga titles with Bayern Munich. With Arsenal still chasing that top-four we expect them to put in a strong performance and so are backing the home win to nil.
After Aleksandar Kolarov's free-kick was pushed behind by visiting goalkeeper Ben Foster and Leroy Sane had dragged wide, City went ahead in the 27th minute with a fine team goal.
As we go into the final stretch of games in the Premier League season, it's not looking as though there is going to be any final day drama.More news: Antonio Conte targets win record after league win
A 2-2 draw for Arsene Wenger's men, coupled with a 3-1 Middlesbrough win over Liverpool would similarly lead to a play-off.
City are now in fourth place, three points ahead of Arsenal.
"We shot ourselves in the foot against Tottenham and we are aware we need to win all the remaining games to be in the race".
Liverpool's result against Middlesbrough would then confirm whether or not the two clubs were playing off for third or fourth place.
"At clubs like Barcelona or Bayern Munich if you do not win you are really out - there you have to win by far".More news: Hamilton Clinches The Spanish Grand Prix
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