Serbia international will spend the rest of the 2016-17 season in Portugal at Sporting.
Markovic is not stranger to Portugal having played for Benfica before earning himself a high profile move to Liverpool in July 2014 under the stewardship of former manager Brendan Rodgers.
The 21-year-old winger has scored three times in 34 appearances since joining the Reds and has struggled ever since his arrival from the Portuguese giants.
Fenerbahce took the Serbia international on a season-long loan deal last season however, Markovic spent the majority of the year in the treatment room following a run of injuries.
The Serbian international winger missed a total of 181 days of football last season due to a series of injuries.
The young winger scored just twice and provided three assists in 20 games for the Istanbul giants over the course of last season.