Mauricio Pochettino had planned to use Juan Foyth as his first-choice right-back this season following the sale of Kieran Trippier to Atletico Madrid.
However, the Argentine suffered an ankle injury in a friendly against Bayern Munich and could be out for a number of weeks.
Pochettino is now considering entering the race for Hysaj, as Spurs prepare to kick off the new season against Aston Villa on Saturday.
Juve boss Maurizio Sarri worked with Hysaj at Napoli and is keen to be reunited with him in Turin.
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