However, Liverpool would likely have competition in the race to sign Bissouma, who joined Brighton from Ligue 1 side Lille in the summer of 2018 for a fee of £15 million.
ESPN claims Manchester United are interested in the midfielder while Monaco and two unnamed La Liga clubs are also weighing up an approach for the Brighton star.
Liverpool should receive a midfield boost in January even if Bissouma doesn’t arrive, though.
Klopp has confirmed Thiago Alcantara, who has struggled with injuries since joining from Bayern Munich in the summer, is close to returning to first-team training.
“We’re already made jokes we should sign Thiago for January, in a good way,” the German said ahead of Liverpool’s clash with Crystal Palace this weekend.
“We cannot rush it — he will not be allowed to rush it. It’s nice to have him on the pitch — he’s not in team training yet, that’s the final step. We’ll see how it is.
“Can he be in team training next week? I don’t know. He has to pass a few tests on the pitch until we make that decision.”