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/1697308004259963319