The Croatian impressed in his first season with Leipzig, helping his side win the DFB-Pokal and reach the Europa League semi-finals.
A recent report indicated that Manchester United were weighing up a move for the 20-year-old, while Chelsea have also been credited with showing interest.
However, according to Nabil Djellit, Tottenham are hoping to sign Gvardiol after making enquiries with Leipzig about the possibility of a transfer.
The centre-back is under contract with Die Roten Bullen until 2026, but Spurs are keen to prise Gvardiol away from Germany as they look to strengthen their defensive options.
Gvardiol featured regularly for Leipzig last season, appearing in 45 games in all competitions, while he also chipped in with a couple of goals.