The Atletico Madrid man has reportedly become the subject of a £21.7m bid from an unnamed Premier League club.
According to Spanish reports the La Liga champions have received a bid for Koke as they prepare to unload a number of players in the summer.
Chelsea are thought to be the favourites to sign the Spaniard after already taking Filipe Luis and Diego Costa from the Vincente Calderon last season.
However it is unknown who made the first move for the winger as Manchester City and Manchester United have also been reportedly linked with a move.
By Phil Wellbrook