The Colombian international was dropped from the Rangers first team squad by manager Giovanni van Bronckhorst following his recent red card against Hibs due to concerns over his motivation and fitness.
The 26-year-old did not travel to the Netherlands for the club's historic win over PSV in the Champions League play-off last week and played no part in the weekend victory over Ross County as he sat out the first match of his suspension.
Morelos, who is in the final year of his contract, was due to sit down for showdown talks with van Bronckhorst this week, but according to a report, the forward has decided that his future lies away from Ibrox.
Turkish outlet Takvim claim that Morelos' agent has opened talks with Fenerbahce over the possibility of a move to the Super Lig outfit, who have been linked with the player in the past, with head coach Jorge Jesus said to be weighing up the proposal.
Morelos has scored 113 times in 228 games for Rangers and is the club's record European goalscorer with 29 goals, having overtaken Ally McCoist's previous record of 22.