The Serbian international has missed 85 days due to injuries and been forced to miss 19 games for the Yellow Canaries as a result.
Fenerbahce had been keen to try and extend their loan deal with Liverpool for another season but have been put off due to recurring injury problems.
The 22-year-old had established himself as a first team regular until his most recent hamstring injury which has seen him ruled out for the past 50 days.
The former Benfica man is however, expected to return after the international break and feature against Osmanlispor.
Fenerbahce are currently second in the Turkish Super League four points behind leaders Besitkas but the Canaries do have a game in hand.
Markovic will return to Liverpool at the end of the season and has been given a chance to prove himself over the pre-season by head coach Jurgen Klopp.
“We had a little talk about things. I said at the start of pre-season you will be very welcome and then it’s up to you,” Klopp was quoted as saying by the Mirror.
“That is how it is in football. It’s a long pre-season and if he wants to come back to Liverpool in July he’s welcome.
“We are short on wingers. Everybody who is involved in pre-season can have a part to play next season. We need a big squad because of the European Championships.