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.
There was a report that Galatasaray bid for the player, but there is no clear proof that the player is interested in joining any team soon. Guardiola was questioned whether there was any possibility that İlkay Gündogan would leave the club this summer, but Guardiola made it clear that Gündogan is their player and that he had never heard anything from him about wishing to go. I don't think Guardiola will lose another midfielder at this time now that De Bruyne has agreed to join Napoli.
However, Gündogan performance in the FIFA Club World Cup against Al Ain was impressive, with two goals, although it is not clear if Manchester City will renew his contract at the end of next season. Pep Guardiola is gathering as many players as he can to improve their performance. Manchester City has bought four midfielders since the start of the transfer window, perhaps if the new players adapt to the league, Gündogan will continue his career in a different team after next season.