Mate, I don't see Real Madrid letting him go on loan anytime soon. Arda is such a game changer for them, though he often gets subbed off. I know his playtime is our main concern. Giving him more minutes is one solution. But he easily starts for mid-table teams in a competitive league.
Arda Guler, will remain a Real Madrid player this season and I doubt there will ever be a reason of loaning him outside this season, since no more Toni Kroos and Modric will soon leave also, it's expected he is among the heritors of the midfield there. In the aspect of injury crisis now, Real Madrid are the club currently looking of adding support players to the team and not selling or loaning their key man this coming transfer window in January.
There's no freaking way to rent him back to Fenerbahce; he deserves to be rented to a bigger club. He needs it to ensure he can step up higher than this time. He is a very promising player to be wasted on a club that wouldn't help develop himself.
Man you spoke as if him moving to Fenerbahçe for a loan deal will be a bad idea, don't forget he will be under Jose Mourinho and also still have a more game time with Europa league football and with Arda Guler, Fenerbahçe will have a better chance of winning the league by being ahead of Galatasaray who is even having a more fearsome squad especially in the aspect of their attack.
I know Fenerbahçe's coach, Mourinho, is a world-class coach. But it doesn't mean it's right destination for Arda Güler to go there. Unless he wants a career suicide, he should stay here, in Real Madrid, as the next upcoming talent. He needs to be developed in a competitive league to form his performance and mentality.
I admit that benching Arda Güler at Real might hinder his development. But there are better loan options for him soon. Anyway, I think he should stay, and i belive he will shine later once he gets a proper club to be loaned. He still has enough time to develop himself. There's no need to rush.