The Argentinian has so far failed to hit the heights expected of him at White Hart Lane following his huge summer move from Roma.
He was handed a start in new full-time boss Tim Sherwood's first Premier League game in charge - the 3-2 win at Southampton - but was substituted after again struggling to make an impact.
There have been plenty of reports suggesting he could go back to Italy - probably only on loan initially - in the new year and Juve are the latest Serie A side to be linked.
Napoli and Inter Milan are also keeping an eye on the situation while there were widespread claims last month that Lamela could join La Liga giants Atletico Madrid on loan in January.
The 21-year-old has started just three Premier League matches and has yet to score in the league, with his only goal coming in a Europa League victory over Sheriff in November.