Real Madrid also bagged a French international star as Eduardo Camavinga arrived from Rennes -- but their attempts to sign Kylian Mbappe from Paris Saint-Germain failed
This year is only the second in 17 that neither Barcelona nor Real Madrid have won the title, the other when Atletico last clinched the league in 2014.
Diego Simeone's side travel to relegation-threatened Valladolid knowing that if they better Real Madrid's result against Villarreal, they will be crowned champions.
"It's a final against Valladolid, with two sides fighting for their own different, but important, objectives and we will both give absolutely everything they've got to achieve it," Simeone told a news conference.
The Catalans practically surrendered their chances of catching La Liga leaders Atletico Madrid after drawing 3-3 at Levante on Tuesday and trail them by four points with two games left.
"It's not fair that one day everything seemed perfect and two weeks later everything is horrible."
But VAR prompted referee Juan Martinez to check an Eder Militao handball a few seconds before, with a huge decision seeing Madrid's penalty cancelled and a spot-kick awarded to Sevilla instead.
Simeone, however, insisted he would not change his usual set-up for a more attacking one.
"Sometimes it's gone really well and sometimes it hasn't. We don't change a lot. We'll try and play using the good points of how we've been playing up to now.