The World Cup-winning captain recently extended his stay in North London until the summer of 2024, by which time he will be 37 years of age.
Spurs do have an option to buy Pierluigi Gollini at the end of the season based on how many games he plays for the club, but Conte has supposedly set his sights on a different shot-stopper.
According to The Sun, 20-year-old Accrington keeper Savin has caught the Italian's eye, with the 6ft 4in keeper featuring regularly for the League One outfit this term.
The report adds that Spurs have sent scouts to monitor Savin's progress, and his performances also led to interest from Southampton in recent months.
Savin has kept six clean sheets in 16 League One games during the 2021-22 season and is contracted to Accrington until the summer of 2023.