Concerns over Alberto Moreno's lack of defensive capability have left the Reds looking for extra depth at full-back and Erkin is thought to fit the bill.
The Toffees recently announced billionaire Farhad Moshiri has taken a major shareholding in the club and are expected to spend money on upgrading areas of their squad this season.
However, they will have to look at other targets with Erkin's switch to Italy apparently wrapped up.
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