BBC Sport says Liverpool have a five-man shortlist including Konate and Kabak as they look to strengthen at centre-back this summer.
France U21 international Konate reportedly has a buyout clause of around 40m euros (£34m).
Liverpool are yet to decide on the future of Turkey's Kabak, 21, who joined on loan from Schalke in January.
They have an option to buy him for £18m - with add-on clauses - but do not need to activate it until June.
Konate was on the bench for the German side in both games as they were beaten 4-0 on aggregate.
He is currently part of the France squad at the European U21 Championship. He did not play in the 1-0 defeat by Denmark but started in the 2-0 victory over Russia.