The Tottenham playmaker is out of contract next June and appears to have no intention of signing an extension in north London.
Eriksen was heavily linked with Real Madrid earlier this summer, but Los Blancos have since moved on to other targets.
And Juventus, who have signed Andrea Pirlo, Paul Pogba, Aaron Ramsey and Dani Alves on free transfers in recent years, want to capture Eriksen for nothing.
That would allow Spurs to keep hold of the Denmark international for the remainder of this season.
Eriksen, a second-half substitute, helped Mauricio Pochettino's side come from behind to beat Aston Villa 3-1 on Saturday.
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