Sabahis reporting that Skrtel - who has 12 months remaining on his contract at the Şükrü Saracoğlu Stadium - has been the subject of a £4 million bid from the Ibrox side.
It was reported earlier this montyh that Steven Gerrard had earmarked his former Anfield team mate as a priority signing.
Burnley midfielder Scott Arfield joined the Gers on a four-year deal yesterday while the club has also been linked with a £4 million swoop for Swansea City forward Oli McBurnie.
Skrtel is understood to have met with the Fenerbahce hierarchy and asked about his situation, with club bosses reportedly telling the Slovakian defender that the decision is all his
The 33-year-old could participate in Fenerbahce’s last match of the season this weekend, at home to Konyaspor.
Fener currently lie in second place, and could take the title if they can beat Konyaspor and current table-toppers Galatasaray - who have the same goal difference as Skrtel’s side - lose to sixth-placed side Goztepe SK.
They recorded a 7-0 win away to basement side Karabukspor last night, with Skrtel playing the full 90 minutes.