To be fair to Klopp, I pulled out a list the top 50 CBs from Transfermarkt (by estimated transfer value), and I got this list:
1 Leonardo Bonucci
2 Mats Hummels
3 Gerard Piqué
4 Jérôme Boateng
5 John Stones
6 Marquinhos
7 Raphaël Varane
8 Toby Alderweireld
9 Eric Bailly
10 Virgil van Dijk
11 Samuel Umtiti
12 Stefan Savic
13 Konstantinos Manolas
14 Kalidou Koulibaly
15 Shkodran Mustafi
16 Nicolás Otamendi
17 David Luiz
18 Javi Martínez
19 Jan Vertonghen
20 Sokratis
21 Stefan de Vrij
22 Aymeric Laporte
23 Antonio Rüdiger
24 Joel Matip
25 Victor Lindelöf
26 Iñigo Martínez
27 Michael Keane
28 Chris Smalling
29 Marcos Rojo
30 Kamil Glik
31 Mateo Musacchio
32 Benedikt Höwedes
33 Daniele Rugani
34 Dejan Lovren
35 Ömer Toprak
36 Mattia Caldara
37 Matthias Ginter
38 Eliaquim Mangala
39 Nacho Fernández
40 Mamadou Sakho
41 Medhi Benatia
42 Ezequiel Garay
43 Jemerson
44 Rúben Semedo
45 John Anthony Brooks
46 Phil Jones
47 Víctor Ruiz
48 Gabriel Paulista
49 Jeison Murillo
50 Simon Kjaer
There aren't very many great options on that list to be honest.
If you exclude Rudiger, Lindelof and Keane, who moved to other clubs, the stand-out options from that list probably are:
van Dijk
Koulibaly
Manolas
De Vrij
Laporte
Ginter
Of that lot, De Vrij, Manolas, Laporte and Ginter are similar to Matip - primarily ball-playing CBs. Whereas Klopp is clearly looking for someone who is aggressive, aerially dominant, and can be a leader at the back. Someone who can replace Lovren and play alongside Matip.
That probably just leaves van Dijk and Koulibaly. Perhaps then the feeling at the club was that it's better to wait, and see if we can get van Dijk in January?
Having said that, I think with Lucas and Sakho leaving, and Gomez moving to RB, there could have been an attempt to bring a talented young CB to at least challenge Klavan's position in the squad.
There are loads of talented u-23 CBs playing across Europe. Maguire, Lascelles, Mawson could have been options from England. Then there are the likes of Tah, Kongolo, Issa Diop, Kimpembe etc.