As per TMW (via Sportwitness), Spurs have been sending signals of their interest to the player for a while now.
Castagne has done well for Atalanta and he would be a good signing for the Londoners.
Furthermore, the 24-year-old has a contract until 2021 and if Leicester were to move for him, they should be able to sign him for a reasonable fee.
Scottish giants Celtic tried to sign him last year and the transfer was close to completion.
Jose Mourinho needs to bring in some competition for Serge Aurier and Castagne fits the profile.