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/1697308004259963319I think it is a good and interesting transfer as Gravenberch has had 25 appearances for Bayern Munich so far and was pretty good I think, but this seems to be a decision by the coach Thomas Tuchel who wanted a different midfielder because he said he has too many of the same kind. But for Klopp this is probably a great addition to his squad as Kopp likes to give younger and hungry players a chance and he knows how to develop them and how to squeeze their potential for the best of the team.
But still there is also risk coming with this transfer as Gravenberch is a great young player, but he is still not this player that you sent on and know 100% what he is going to do. He has had minor mistakes if I recall that correctly and the Premier League with Liverpool is different than playing the Bundesliga with Bayern Munich.