The 24-year-old defensive midfielder joined Leicester in the summer of 2021 from French outfit Lille.
Soumare is attracting interest from several clubs and Spanish outfit Sevilla and Turkish giants Galatasaray are keen on him.
It has been suggested that both clubs are in negotiations with Leicester in order to agree a deal for Soumare.
Now Fenerbahce have joined the race for the signature of the Leicester midfielder, according to Turkish outlet Spor.
Fenerbahce want to end their Turkish Super Lig title drought this season and believe that Soumare will strengthen their midfield.
Soumare featured 26 times last season while picking up nine cautions, but failed to help Leicester avoid relegation.
The defensive midfielder has three years left on his contract but is keen to leave the King Power Stadium this summer.
Soumare has not featured for Leicester so far this season and now it remains to be whether the Frenchman will be able seal an exit this summer.
