The Reds are planning for life after German head coach Jurgen Klopp departs.
However, Sky Sports state that the Anfield decision makers are going in a different direction.
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They are looking at Inter Milan's Simone Inzaghi or Sporting CP's Ruben Amorim.
De Zerbi may still have other tempting offers to take him away from Brighton.
He is said to be on the radar for Bayern Munich, while he has been linked to Barcelona recently as well.