They will go and offer him a new contract, but there is no point in during it early or before Christmas. He is in the form of his life and the goal is to motivate to continue in the form of his life and then he will for sure receive his well deserved offer for a new great contract.
But rest assured that other clubs have long reached to Salah's managers. That's the most normal thing and negotiations or at least slight requests are probably going back and forth for a while now as everyone knows that he will be without contract soon. It would be dumb to not try their luck and Real Madrid could be one of the clubs that would be willing to give Mo Salah one big contract for maybe 3 years. He isn't the youngest anymore, but he is fit and fast as always. Would be a good pick for any club.
If Mohammed Salah leaves Liverpool, forget this hype Arne Slot is having, their performance will change and they will drop from that top of the table they are using to be champions. After Haaland, the next highest goal scorer is Salah and they are not even far from each other due to Manchester City not been stable with their own performance. There is going to be affirmation of Salah staying in Liverpool even if they are going to win this Premier League before going to another club.
I'm also contemplating which club such an amazing player will like to go, he is too good to be heading to Saudi Arabia but i know him for one thing, the Arabs cherish him very well, so there is high chance that they are in the journey of bringing him to Saudi Arabia perhaps to Al Nasr where his ex play mate is playing, they will make a great combo but it wouldn't be palatable because of the presence of Ronaldo, it will be a congested team and at the end, they will not win anything.
Liverpool has proven a couple of times that they can find players to replace former superstars. When they had Sadio Mane, Salah etc. and Mane left, some people said that he was so important to the game of Salah and it would be difficult to replicate that with another player. But they did it and they did it successfully. Klopp got all these new guys on board like Nunez, Diaz, Jota, Gakpo, so I am not concerned that Liverpool wouldn't be able to either find a new player on a very high level who is immediately ready to jump in because who wouldn't want to play for Liverpool these days?
Then they can still use the players they already have because they are playing well already. All the aforementioned players are an important part of the team today and will be in the future.