A few weeks ago the Champions League race looked over, but seven Premier League wins in a row have put Liverpool back in contention.
Manchester City and Arsenal are assured of a top-four finish, with Newcastle and Manchester United looking the most likely to join them.
The Magpies took a big step towards clinching Champions League qualification with victory over Brighton on Thursday – although Eddie Howe said they are “not looking too far ahead” after the game.
Liverpool are just one point behind Manchester United, but have played one game more than the Red Devils.
“I don’t think it [a Champions League spot] is likely, but if they slip we have to be there,” said manager Jurgen Klopp after their 3-0 win over Leicester on Monday. “Will they slip? I don’t know. Will we win both games? I don’t know.”
The sides that finish in the top seven will secure some form of European football next season – BBC Sport takes a look at how things are shaping up.
Who can finish in the Champions League places?
Manchester City, who could win the Champions League this season, and Arsenal, with their current totals of 85 and 81 points respectively, will finish as the top two.
City will win the league if they beat Chelsea on Sunday (16:00 BST).
Third-placed Newcastle, on 69 points, need to win just one of their remaining two matches to secure a place in the top four.
Manchester United are fourth on 66 points, but Liverpool remain within touching distance just one point behind in fifth.
Liverpool were 12 points behind on 9 April, but their recent resurgence has kept them in the mix – while Manchester United have won only one of their past three games.
According to data experts Nielsen’s Gracenote, Newcastle now have a 91% chance of finishing in the top four, while Manchester United have an 80% probability.
Newcastle’s win over Brighton means Liverpool’s chances have dropped from 45% to 30%.
If Manchester City go on to win the Champions League, whoever finishes fifth in the Premier League will not gain qualification to next year’s competition as a result.
The only circumstances under which five English teams could qualify for the Champions League is if a Premier League club wins the competition but then fails to finish inside the top four in the top flight.
What about the Europa League?
The teams that finish fifth and sixth in the Premier League are guaranteed a place in the Europa League, because FA Cup finalists Manchester City and Manchester United will finish in the top six.
Liverpool currently occupy fifth position – although their sights are higher now.
They are seven points clear of sixth-placed Brighton, who have a game in hand, with Tottenham and Aston Villa just one point behind Albion.
“Liverpool and Brighton remain the most likely teams to play in next season’s Europa League group phase according to the Euro Club Index,” said Simon Gleave, head of sports analysis at Nielsen’s Gracenote.
What about the Europa Conference League?
The team who finish seventh will go into the Europa Conference League play-offs, because Carabao Cup winners Manchester United are guaranteed at least a Europa League spot through the league or FA Cup.
That place is almost certain to go to one of the teams already mentioned in the fight for a Europa League place, with Nielsen’s Gracenote making Tottenham 58% favourites. Ninth-placed Brentford, who have 53 points, have a 1% chance.
How could there be eight English teams in Europe next season?
West Ham are well out of the picture for a top-half finish but have reached the Europa Conference League final.
If they win that competition they will earn a place in the group stage of next season’s Europa League.
The Hammers will face Italian side Fiorentina in the final in Prague on 7 June – and are slight favourites with a 56% chance of winning the competition, according to Nielsen’s Gracenote.