Jose Mourinho has much work to do in Fenerbahçe. Don't forget that last season, the club finished second and qualified for a European championship. Currently, the Special One has managed to take them to the fourth position, which is below expectations.
Arda Guler deserves more playing time which he will not get in Real Madrid currently. The number of stars in Madrid will always relegate this gifted Turkish star to the bench. Maybe Mourinho wants to use the opportunity to get the player on loan because Real will not be willing to let him leave permanently. The player is seen as the future of Real Madrid, so they will want him to come back when there is an opening for him. Galatasaray got Victor Osimhen cheaply, but I doubt if Los Blancos will let Guler leave without any financial obligations to the Spanish side.
While I agree about Arda Guler needing more playing time to improve, there is a balance in this kind of situation for younger players. Meaning, Arda would improve himself a lot more if he stayed at Real Madrid and play only on some games and only on later stages of the game, he still gets 15-20 minutes a game in most games unless it's a very close or important game, we see him play there time to time, not a lot of minutes, not as much as he needs to play, he needs to play a lot more.
However, if he goes to Fenerbahce, this would be a team he can play all 90 minutes every game and he still wouldn't improve as much as he improves just from training at Real Madrid, he can't drop that low, he needs to be loaned to a team at least in UCL, not back to Turkey.