Klopp has some things going under his sleeve, it will be a wasted effort if he doesn't signed any player now. However, seeing that they don't have any business in the Champions League this season, he might want to wait and observe how his boys are going to perform in the Premier League and then make some changes by January transfer period.
They have signed Ryan Gravenberch near the deadline day from Bayern which I think is a great move
[1] . They need some fresh players and I feel they have filled in with some good midfielders with potential. Still they are not yet consistent but I believe as the season moves on they will become more consistent. This season they have to make it in CL because that is the minimum standard for a team like that.
References :[1]
https://twitter.com/FabrizioRomano/status/1697308004259963319Liverpool have to compete with Manchester United to gets him and even Manchester United is very serious and they were already contact Bayern Munich first before Liverpool but apparently Gravenberch was more interested to joining Liverpool than Manchester United and recently Gravenberch has been done medical check and he will gets long term duration contract until 2028 and actually Gravenberch is good player because while playing at Ajax he can able to showing impressive performance so that's why Bayern Munich was decide to bought him but unfortunately he failed to earn Nagelsmann trust and had lack of minutes of play
Just like i said before Gravenberch is really want to leave Bayern Munich because he want to gets more minutes to play and i think he has made good decision with moved to Liverpool and now Klopp has several options for midfielder and besides that Gravenberch can be played as holding midfielder just like when he was playing with Ajax so Gravenberch is very suitable as the replacement of Fabinho who leaved Liverpool