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And the more important problem is that you need to find an outstanding coach who is willing to manage a team that does not play Champions League. That is a huge issue for Chelsea. I read that Nagelsmann was already there, but in Nagelsmann's case it makes more sense to wait and see if another Champions League club wants him. It could be Real Madrid, it could be Barcelona, the incentive to sign a contract with Chelsea right now is not that high unless the salary is unprecedented.
Chelsea Job needs a Manager who does not believe or depends on their past history, or be treathened by their current poor situation, or reject it because they didn't qualify for next season's Uefa champions / Europa League. All they need is a Manager who will focus on the club goals, that will try his possible best to bring back the club to its position, although it looks difficult on this time because many managers will be scared of their club and fans high expectations. Looking at the club current situation, it need both players and other technical coaches to sit up and put in their best in the coming season to enable the team meet their goals.