Atletico should have plenty of money available after talismanic striker Antoine Griezmann said last month he is to leave the club.
Four goals from Zlatan Ibrahimovic spurred Paris St Germain to their fourth successive Ligue 1 title with a 9-0 rout of Troyes, becoming the first team to win the championship after 30 matches.
Paris St Germain would be odds-on certainties to easily beat Chelsea and take a big step towards the Champions League quarter-finals on Tuesday if statistics and domestic form decided matches.
There was the usual frenzy of last-minute deals as the English Premier League brought the curtain down on another bumper European transfer window in which Manchester City again flexed their financial muscle as the continent's top spenders.
Striker Costa ends second spell at Atletico Madrid.
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