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Liverpool didn't fire Jurgen Klopp because Klopp decided to retire himself so I think Liverpool still has a good relationship with Klopp. In my opinion, there is a possibility that Arne Slot will be selected because of Klopp's suggestion. For the first stage, Liverpool cannot hope to achieve good results in the UCL and EPL. Arne Slot also requires tactical adaptation to each Liverpool player. Every coach has a different way even though they have the same philosophy. In modern football I don't think big names make much of an impact. A coach must be able to adapt to various variations of tactics and watch replays of each opponent's game. I think a flexible coach is the coach Liverpool needs right now.
Nobody said Liverpool fired Jurgen Kloop, we all know that Kloop's departure from Liverpool was his own desire to stop being a football coach and wanted to rest for a while, with the decision taken by Jurgen Kloop, Liverpool could not force their will to continue being trained by this coach or at least until the contract expires, every coach can make decisions at any time because they have the authority to make their own decisions without coercion. So even though they have officially separated, there is no reason why Liverpool and the former coach are not on good terms until now.
In Arne Slot's first season with Liverpool, it certainly requires adaptation between coaches and players, it's not easy to immediately perform optimally, it requires appropriate tactics so that the club can appear impressive, but I think the new coach will try as hard as possible so that Liverpool's performance doesn't decline, at least it doesn't have to produce positive results winning the title, at least competing with top clubs, Liverpool can compensate for that. I think Liverpool's good results in the Champions League next season could reach the semifinals, or reaching the quarter-finals the Champions League would be better if they could reach the final but I think it was quite difficult in the first season.