Turkish journalist Yagiz Sabuncuoglu claims that the two clubs sent scouts to watch 18-year-old goalkeeper Berke Ozer ahead of a possible swoop for the player in the summer transfer window.
Ozer was playing in the U21 derby match between Fenerbahce and Galatasaray, during which he kept a clean sheet in a 0-0 draw.
Ozer was linked with a switch to Manchester City before he joined Fenerbahce from his boyhood club Altinordu in a €2.5m deal.
Whilst he has only made one appearance for the senior side thus far, he regularly plays for Turkish youth national teams and has looked particularly impressive in recent months.