The daily Turkish newspaper Takvim states that the Istanbul Giants will table an offer when they meet with the Merseyside club.
The Serbian international joined Fenerbahçe on a one-year loan from Liverpool over the summer transfer window and has already established himself as a first team regular.
Markovic joined Liverpool in 2014 after being tipped as one of the hottest properties in European football, but has failed to make any significant impact. The 21-year-old scored three goals and provided one assist in 34 appearances for the Red’s last season.
The former Benfica forward has two assists and one goal for Fenerbahce this season.
Fenerbahce take on Eskisheirspor in their next Turkish Super Lig encounter while Liverpool take on Stoke on the Carlin Cup semi-final tonight.