Without a club since the end of December, the former Chelsea marksman could make a sensational return to the English top-flight.
Diego Costa has been approached by a top-six Premier League side, according to Sky Sports.
Costa, who is available on a free transfer, has been offered a deal until the end of the season by the unnamed Premier League club.
The mystery club could be any one of Manchester City, Manchester United, Liverpool, Leicester City, West Ham United, or Tottenham as those make the top-six in the league standings currently.
However, there exists a difference in the demands of the player and what he has been offered.
The 32-year-old striker, who is also attracting interest from clubs in Turkey, Qatar, and Saudi Arabia, wants a contract for at least 18 months worth around £13m over its duration.
Costa was released by Atletico Madrid at the end of December and has been a free agent ever since. He spent three years at Chelsea, scoring 29 goals in 120 appearances and winning the Premier League title twice, in between his stints at Atletico.
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