£20million Markovic has received interest from Greek side PAOK, but the Serbian international has also been discussing moves to Standard Leige or Anderlecht.
The 24-year-old is reportedly interested in the move to Greece if PAOK are able to strike the right deal with Liverpool.
Markovic made the move to Liverpool four years ago, but failed to make a real impact for the Reds.
He was loaned out to Fenerbahce, Sporting, Hull and Anderlecht.
His arrival at Anderlecht was a disaster, as the side said that the Serbian's fitness and condition was so poor that he would have to miss up to six weeks to get up to standard.