If Arsenal win their remaining games, they will finish on 74 points.
London: Arsenal manager Arsene Wenger believes that if his team win their last three Premier League games they will qualify for the Champions League, but both Chelsea and Tottenham Hotspur could yet scupper his hopes.
If Chelsea take at least nine points from their last four games, they will finish on 74 points. If Tottenham win their four remaining games, they would also finish on 74 points.
However, even if Arsenal win their remaining games against relegated Queens Park Rangers, Wigan Athletic and Newcastle United, they would finish on 73 points and could miss out on a place in the Champions League for the first time in 16 years.
The key game is on May 8 when former Chelsea manager Andre Villas-Boas takes his Spurs team to Stamford Bridge to face his old club.
If Spurs win that game and their other three remaining games against Southampton, Stoke City and Sunderland, they will finish above Arsenal.
Chelsea will also finish above Arsenal even if they lose to Spurs and win their three other games at Manchester United and Aston Villa, and at home to Everton.
As it stands, champions Manchester United and Manchester City, who will almost certainly finish second, will take two of the four Champions League spots.
Next come Chelsea on 65 points from 34 games, followed by Arsenal (64 points from 35 games) and Spurs (62 points from 34 games). Everton (59 points) also have a mathematical chance of finishing in the top four and have three matches to play.
Wenger saw his side drop two points in a 1-1 draw with champions Manchester United at the Emirates Stadium on Sunday and said afterwards there was no more room for errors as the season reaches its climax.
Asked whether the point would be enough for Champions League qualification for a 16th successive season, Wenger replied "If we win all our games it will be enough and I am convinced we will be there. We will be where we want to be at the end, I am sure of that.
"But you know there is no room for dropping points. We know that."
Arsenal slipped from third to fourth in the table after Chelsea's 2-0 home win over Swansea City on Sunday, while Tottenham Hotspur remained fifth after a 2-2 draw at Wigan Athletic on Saturday.
Wenger welcomed the return of former Arsenal skipper Robin van Persie back to the Emirates, even though he scored a penalty to give United a share of the points.
Arsenal fans booed their former favourite despite Wenger's plea for him to be treated with respect.
"When he was here he didn't get that kind of reception," the Frenchman added. "They loved him - today it was a bit of disappointed love."
Wenger also laughed off Van Persie's goal, saying "He scored a penalty but it is not completely the same as scoring.
"He takes penalties very well and when he decided to take the penalty I knew there was an 80 percent chance he would score.
"Robin van Persie does a lot of things very well."
Theo Walcott put Arsenal ahead after two minutes before Van Persie equalised a minute before halftime.