The 21-year-old centre half has become a mainstay in the team next to Virgil Van Dijk.
Even when the likes of Ibrahima Konate are fit, Quansah is often the starting defender.
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Per The Mirror, the Reds will open talks with the England U21 international's agency CAA Base.
However, they will also push to sign a left-footed defender for new boss Arne Slot.
Eintracht Frankfurt's 22-year-old Colombian Willian Pacho is one of the mentioned names.