I think not any personal verbal agreement reached between Barcelona and İlkay Gündoğan, actually Manchester City success signing Chelsea midfielder Mateo Kovačić will replace position leaving İlkay Gündoğan but still not confirm yet which one team will play next season. Not only Barcelona but also Arsenal and PSG has announced interested for signing İlkay Gündoğan next season.
City have agreed personal terms with Chelsea's Kovacic, but the deal isn't done yet because Chelsea and City haven't discussed on the transfer fee yet, they'd do that after the CL final, having said that i don't think City want Kovacic to be a direct replacement for Gundogan because there is an offer on the table for him, one he might agree to after the CL final tomorrow.
Barcelona have not opened any talks with Gundogan and his agent yet, they will have to wait until after the CL final, then Gundogan will make a decision to either stay or leave, that is when talks can take place if he decides to go.