Leicester and Tottenham are guaranteed automatic qualification to the Champions League next season, but seven other Premier League clubs are waiting to learn their fate as the race for the European places reaches a climax.
The Premier League is given four spots in the Champions League, with the top three going into the group stages and the team in fourth earning a place in the final qualifying round.
There are then three spots in the Europa League which are awarded to the team who finish fifth, along with the winners of the Capital One Cup and the FA Cup.
This year, however, Capital One Cup winners Manchester City can finish no lower than fifth, so that Europa League place will go to the team in sixth.
That means fifth, sixth and the FA Cup winners will qualify for the Europa League. If Manchester United win the FA Cup and finish in the top six, however, then the team who finish seventh will also earn a spot in the Europa League's third qualifying round.
The situation could be further complicated by Liverpool, who cannot finish in the top four but will become the fifth Premier League team to qualify for the Champions League if they beat Sevilla in next week's Europa League final.
If Liverpool win the Europa League and finish in the top seven, then the Premier League is likely to lose one of its spots in next year's Europa League, meaning seventh place is not a guarantee of European qualification.
But in the event that Liverpool win the Europa League and finish eighth, the Premier League would be represented in Europe by eight teams - five in the Champions League and three in the Europa.
Another scenario in which the Premier League could have eight teams in Europe is if Crystal Palace win the FA Cup and Liverpool win the Europa League and finish seventh.
Here, we examine the permutations for each of the contenders...
3rd. ARSENAL (68 pts, +25 GD)
Remaining game: Aston Villa (h)
Form: DWDWDD (Most recent first)
Arsenal's 2-2 draw with Manchester City on Super Sunday means they will clinch a top-three finish and go straight into the Champions League group stages as long as they avoid defeat to rock-bottom Aston Villa on the final day of the season.
The Gunners are guaranteed a top-four spot following Manchester United's defeat to West Ham on Tuesday.
Arsene Wenger's men are huge favourites to beat Villa, who have lost 11 of their last 12 games, and they could even pip north London rivals Tottenham to second place if Mauricio Pochettino's team are beaten by Newcastle at St James' Park.
4th. MANCHESTER CITY (65 pts, +30 GD)
Remaining game: Swansea (a)
Form: DLWDDD (Most recent first)
After having their top-four bid taken out of their hands by a 2-2 draw with Arsenal on Sunday, Manchester City were grateful to West Ham for beating Manchester United. That result means City will guarantee a top-four finish if they win or draw at Swansea on the final day.
Regardless of whether City finish third, fourth or fifth, the Europa League spot they earned for winning the Capital One Cup will go to the next highest Premier League finisher not to have qualified via a cup competition.
5th. MANCHESTER UNITED (63 pts, +12 GD)
Remaining games: Bournemouth (h), Crystal Palace (FA Cup final)
Form: LWDWWL (Most recent first)
United's Champions League destiny was in their own hands, but defeat at West Ham means they are now reliant on Manchester City losing against Swansea on the final day.
If City are beaten then United will finish fourth as long as they win their home game against Bournemouth.
Louis van Gaal's men could also end up in the Europa League if they finish fifth, sixth or seventh or beat Crystal Palace in the FA Cup final.
A worst-case scenario for United would be to lose their last league game and the FA Cup final, with Liverpool, West Ham and Southampton claiming maximum points. If Liverpool then win the Europa League, United would miss out on European football altogether next season.
6th. WEST HAM (62 pts, +15 GD)
Remaining games: Stoke (a)
Form: WLWWDD (Most recent first)
Manchester City's vastly superior goal difference means West Ham's hopes of mounting a late challenge for the Champions League spots were ended by their 4-1 defeat to Swansea last time out.
But Slaven Bilic's men did boost their chances of being in the Europa League by beating Manchester United on Tuesday. The Hammers could finish above United in fifth, therefore going straight into the Europa League group stages, if results on the final day go their way.
7th. SOUTHAMPTON (60 pts, +15 GD)
Remaining game: Crystal Palace (h)
Form: WWWDWL (Most recent first)
The Champions League is out of reach for Southampton but they will fancy their chances of making the Europa League. Ronald Koeman's men dropped back to seventh after West Ham beat Manchester United, but that is still enough to go into the Europa League qualifying round - unless Crystal Palace win the FA Cup, or Manchester United win it and finish eighth.
As for their own game at home to Crystal Palace, the in-form Saints will be confident of taking three points. Alan Pardew could rest key players with the FA Cup final in mind, and if United lose their remaining games, Southampton could even move up to fifth on goal difference by beating the Eagles.
8th. LIVERPOOL (59 pts, +13 GD)
Remaining games: West Brom (a), Sevilla (Europa League final)
Form: DWLDWW (Most recent first)
Liverpool are too far short of the top four to clinch a Champions League spot through their Premier League finish, but they could book a place in Europe's elite competition by winning next week's Europa League final against Sevilla.
Defeat to Sevilla and an eighth-placed Premier League finish would see Liverpool miss out on European qualification altogether, but Jurgen Klopp's men can still climb up the table to sixth and secure Europa qualification even if they lose to Sevilla.
14th. CRYSTAL PALACE (42 pts, -9 GD)
Remaining games: Southampton (a), Manchester United (FA Cup final)
Form: WLLDDW (Most recent first)
Crystal Palace have spent much of the season battling against relegation from the Premier League but Pardew's men would go straight into the Europa League group stages if they beat Manchester United in the FA Cup final.