Klopp will not be sacked by Liverpool management, this is a trying times for Klopp and Liverpool, every team do have trying times. They have to be patience with him. Klopp is an experienced coach and if Madrid bid for him, is not a bad either he will deliver the club.
Klop hasn't had any successful results this season. I agree with that. Everyone agrees with this opinion. But if Klopp leaves, who will they entrust the team to? I think it would be a big mistake to send Klop off the team. Chelsea made the same mistake. They sent Thomas Tuchel and made a deal with Graham Potter to replace him, but now they are in a worse situation. I think if Liverpool send Klopp out of the team, they will suffer the same fate as Chelsea.
After sacking of Thomas Tuchal how things gone in Chelsea all are aware and with having good record at club in past just one season is going into wrong way most chances Liverpool management will not do anything like this because they are also having feeling things like these can happen so giving him more time is enough instead of having worst like Chelsea which is surely now going deepen because they are still not able to have positive results even against weaker sides.
As they are having bad time, but things can go better it's matter of just sometime or having some change in strategy now after win against Everton surely they are feeling positive and can do better against Newcastle United and Real Madrid which will bring good changes, and they will be on right way for the better end of this season.
As you are mentioning Thomas Tuchel here, it just came to my mind what could be going on next season when one of the coaches like Klopp or Simeone gets sacked. Liverpool would be looking for a coach, Madrid might be looking for a coach and even Atletico might be looking for a coach. We may see a lot of back and forth between the clubs and the available coaches. Unless Ancelotti wins the Champions League, I don't think he will remain the coach of Real Madrid for another season. Zidane is also available as far as I know.