The midfielder is being linked with a move to European giants Juventus and Liverpool.
While both clubs are eager to secure his signature, Atalanta also hope he will stay.
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Per Tutto Juve, incoming Reds boss Arne Slot could be a deciding factor in the situation.
Koopmeiners is said to want to play for Slot and in his system, which would give the Reds an advantage.
They also have greater financial muscle, as compared to Italian side Juventus.