Markovic will be out for another two weeks with injury a source close to the club told Turkish-football.com.
The Serbian international has been out for the last month with injury and was expected to return last week but his recovery has taken longer than expected.
Jurgen Klopp has confirmed Markovic will be given the chance to secure a place in Liverpool’s squad next season.
The Serbia international was in Liverpool last week holding talks about his future but has since returned to Turkey.
Markovic joined Liverpool for £20 million from Benfica in the summer of 2014 but endured a disappointing campaign and was sent on loan to Fenerbahce.
“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.
Fenerbahce take on Braga on Thursday at the Sukru Saracoglu stadium. The Yellow Canaries are currently first in the league and have booked a place in the Turkish Cup semi-final.