I think Rodrygo will stay at Real Madrid even though he will likely only be a substitute in the future, that's because Man City still hasn't found a clear point regarding Savinho agreement with Tottenham and as far as I know Man City is currently more focused on recruiting Donnarumma, with the transfer window closing soon, it means they don't have enough time to recruit both of them.
I do not support Rodrygo to remain at Real Madrid this season because it is very clear that he will not be having enough playing time in the team as the coach is not including him in his plans for the team. If Manchester City is focused on bringing Donnarumma to the team the best thing if for him to look for another team that will sign him while Real Madrid will reduce the amount placed on him if they want him to be sold out.