It seems that İlkay Gündoğan has no intention of going anywhere. Galatasaray wanted him very much, but after yesterday's game he made a statement that I have a contract for one more season and I'm very happy here. I believe I have a few more years at the top level, he said, which shows that he doesn't want to leave the Top 5 leagues.
If Manchester City decide to let him go again, his new club will be at least as strong as Barca. I don't think he will go to Galatasaray and I don't think City will give him to other Premier League teams either. He may struggle to keep up with the pace, but he still has a lot to offer. He didn't miss a game last season.
İlkay Gündoğan still really wants to play with Manchester City maybe until the end of his contract and after that it is very likely that İlkay Gündoğan will not be in a team that plays in the top European league.
İlkay Gündoğan is already 34 years old and if he stays for another season with Manchester City then next season he will be 35 years old so realistically a 35 year old footballer will not be able to perform optimally to compete with young players so maybe İlkay Gündoğan now just wants to enjoy his last moments playing at the highest level of football.