Despite only losing three games this season across all competitions, the 35-year-old German was fired from Bayern Munich on Friday afternoon.
Both the Spurs board and Kane have high hopes for Nagelsmann as the club enters a pivotal phase in its search for Conte’s successor.
The spurs might hire Ryan Mason as a caretaker manager until the end of the season and then find a permanent replacement in the offseason.
After his most recent goal in England’s 2-1 win over Italy, Kane surpassed Wayne Rooney as the country’s all-time leading goalscorer with 54.
Kane came up through the Tottenham system and has remained with the club for his whole professional career, during which he has made 425 appearances and scored 271 goals.