The 30-year-old arrived amid much fanfare last term, but is not in the plans of new coach Rafa Benitez.
Rodriguez still has a year left on the two-year contract he signed last summer.
But there is no imminent move, as Everton have not received any significant inquiries for the attacking midfielder.
Rodriguez recently said on his Twitch account: "I would like to play wherever they want me, I already played in all the leagues.
"I am missing Italy, it would be a good option."
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