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.
Jurgen Klopp reach mutual contract with Liverpool and his decision retired awhile as manager, seems Jurgen Klopp had contribution behind appointing Arne Slot become new Liverpool manager for next season and bring back get good achievement in Champion League after success winning one UCL trophy under Jurgen Klopp era and twice moment lead to final season 2021/22 before beating by Real Madrid.
Liverpool with new manager next season I believe although had recommended from jurgen Klopp but Arne Slot has own tactician and more difference with Jurgen Klopp tactician, next season looking the opportunity some regular player under Jurgen Klopp era will loss their regular position because each manage has their own tactician and favorite players will get regular position every match. I won't to see Liverpool under Dutch manager era get the same with Manchester United when appointing Erik ten Hag got failure their performance in Champion League, as fans huge expected to see Liverpool after missing one season appearance in Champion League can reach higher round for next season exactly until final round.