Greek media sources say Tottenham's scouting and analysis department holds Tzolis in high regard.
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Spurs management sees the 23-year-old as a player with the potential to develop into a future star.
Club Brugge are demanding around £35m to release him. Crystal Palace are also said to be monitoring the player.
Tzolis has been in strong form, scoring 16 goals and providing nine assists in all competitions last season.