Mateo Kovacic has been very instrumental to Chelsea's success since he joined the club from Real Madrid. It'll be a very wrong decision from the club management of Chelsea to let him join another English club.
Chelsea has been letting go of the important players if the club this summer but are yet to make significant signings to replace the players that are leaving the club and if nothing is done about it, it'll surely affect them by next season
This is none other than their poor performance this season which has made them leave Chelsea and go to another team like Mateo Kovacic did. There is no way for the chelsea management to hold him back if the player wants to go to another team even though he is a very important player for them. Mateo Kovacic is certainly not the first player to leave Chelsea this season I think some of the other players will go to other teams if they get offers from other teams.
Apart from that, I think it was Pep Guardiola who convinced him to move to Manchester City next season. I think this progress will be completed after the champions league final and we will see an official announcement regarding the transfer of Mateo Kovacic.