The Greece international has peaked the interest of clubs across Europe and his club resisted a £5 million bid from Genoa in January.
Teamtalk has now reported that four English top-flight clubs - Leicester City, Everton, West Ham United and Newcastle United – sent scouts to watch the 23-year-old in action for his country on Saturday.
The full-back played the full 90 minutes as Greece defeated Liechtenstein 2-0 in Vaduz to begin their Euro 2020 qualifying campaign.
Koutrisa will be watched a second time when his country travel to face Bosnia and Herzegovina on Tuesday night.
The Brazil-born defender has made 22 appearances in all competitions for Olympiakos this season, providing four assists.
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