Amartey, 28, joined the Foxes in 2016 from FC Copenhagen for a fee worth £6m.
He has so far made 106 league appearances for Leicester since his arrival at the King Power Stadium.
The Ghanaian played in 24 matches in all competitions for the Foxes this season and was booked only once.
The 28-year-old centre-back saw his involvement on the pitch hugely restricted after January and found his name in the starting eleven just three times after February.
Now, following his side’s relegation from the English top flight, the Ghana international is expected to be part of a potential exodus from the King Power Stadium.
And according to Turkish outlet Sports Digitale, Besiktas are in talks with Amartey as the Turkish outfit are eyeing bolstering their defensive ranks ahead of next season’s campaign.
It is also suggested that before the talks were held, Gunes received information about the Ghanaian from his compatriot Soyuncu.
It remains to be seen now whether Besiktas will be able to strike a deal for Amartey this summer.
