I think Arda should seriously consider going to another team like Nico Paz instead of being a substitute for his own future. He has the talent to be a starter in most teams he goes to today. The last I heard was that Xabi Alonso also wants him. I think he can try his luck at Leverkusen on loan in January.
It can happen if the player wants and the club also wants. But Madrid has made a statement that Arda Guler will continue to play in Madrid, which means Ancelotti still needs him as part of the team's plan. He still has a little chance to play, he is still young and I think Ancelotti will give him more chances in the future. For now, he is fine in Madrid, maybe it would be very good for him to be the first choice in the squad that he can get in another club. But being a young player in the Madrid squad will not be easy.
Real Madrid has already stated that Arda Guler is an important asset for them, and any offer is likely to be rejected unless it is a loan option. But, if we look at how many players are prone to injury this season, it looks like Real Madrid will really need Guler at this time and it seems that Guler is also quite comfortable with his current situation. If Guler wants the big stage then he has to be patient, but if he is in a hurry then the only way is to leave Madrid (whether it is permanent or with a loan option).
You are right, when Arda Guler is patient, then he will get his big stage in the future with Madrid. Madrid sees the great potential that Arda Guler has even though he is still young. Therefore Madrid is willing to contract him for the long term. He is really an asset for Madrid. In the future when he grows even greater, his market value will be very expensive.
At least for this season, Arda will be with Madrid. As you said with the current condition of the Madrid team he is very much needed in the team. We do not know their situation next season, but the opportunity to be loaned may be available.