Liverpool boss Brendan Rodgers is looking to reinforce his defensive options in the January transfer window.
Liverpool defender Jose Enrique is expected to be out of action with a knee problem until next year and Rosger is keen to bring in a new full-back in January.
Erkin has impressed for Fenerbahce this season and could join Liverpool in a cut-price deal in January, as his contract with the Turkish side is set to expire in the summer.