Liverpool top brass flew Michael Edwards to the United States last week to bring him back to the club.
Edwards was previously the sporting director at the Anfield club until he left in 2022.
Having worked in that role from 2016, the Reds would love to have Edwards back at the helm.
However, Liverpool Echo states that he is reluctant to take on the same role as before.
He is now hoping that he will be offered a bigger role within the club's setup.
Liverpool will also be searching for a new manager this summer, with Xabi Alonso the favorite for the job.