The Turkish outlet states that the 22-year-old’s agent approached Galatasaray representatives and stated that his client would be open to a move to the Lion’s.
Markovic spent last season on loan at Galatasaray’s bitter rivals Fenerbahce which would make such a move controversial.
The Serbian international joined Fenerbahce on-loan last summer amid high expectations and despite getting off to an impressive start working his way into the first team he had a nightmarish season with injuries.
Markovic suffered four injuries and only recently returned to football after 140 days on the sidelines before picking up a hamstring strain during training for his national team.
The 22-year-old will miss Euro 2016 as a result of his latest injury and a return date has not yet been set.