The midfielder, 32, has just been released by Sevilla.
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Tribalfootball.com's transfer expert Rudy Galetti is reporting AEK are in talks with the Argentine.
Galetti states: "AEK sent an official offer to Erik Lamela: a 3-year contract on the table for a free-agent transfer.
"The Argentine player - who is evaluating the proposal - will give a response within the next 48 hours as @urieliugt said."