Eriksen, 27, has made clear his desire to leave Spurs for a new challenge and has been repeatedly linked with moves to Spain's biggest clubs - Real Madrid chief among them.
The Danish midfielder has entered the last 12 months of his contract at Tottenham, meaning other clubs are free to talk to him in January.
The Daily Mail's Italian journalist Alvise Cagnazzo reported Juve are monitoring his situation closely with a view to snapping him up on a free transfer at the end of this season.
The Italian giants have developed a penchant for signing top talent on free transfers in recent years, particularly in midfield.
Fabio Cannavaro (Real Madrid), Andrea Pirlo (AC Milan), Paul Pogba (Manchester United), Fernando Llorente (Athletic Bilbao), Kingsley Coman (Paris Saint-Germain), Sami Khedira (Real Madrid), Dani Alves (Barcelona), Emre Can (Liverpool) and in this transfer window Aaron Ramsey (Arsenal) and Adrien Rabiot (PSG) all joined the Old Lady without transfer fees.
Eriksen, an Ajax youth academy graduate, was omitted from Spurs' starting XI for their opening Premier League win against Aston Villa but was dangerous when introduced off the bench.
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