Kane remained with the Lilywhites over the summer despite persistent links with Manchester City, although the England captain is not expected to stick around if Spurs end another season without a trophy.
Antonio Conte's side are thought to be one of several clubs interested in a deal for Vlahovic, who will not be extending his contract with La Viola beyond 2023.
According to Marca, Conte has personally identified Vlahovic as the ideal man to fill Kane's boots should he complete an expected move elsewhere in 2022.
Spurs will likely have to fend off interest from Man City, Manchester United, Newcastle United and Juventus to sign Vlahovic, though, and Fiorentina are thought to be after £55m to sanction a January sale.
Vlahovic's strike in the recent defeat to Empoli took him to 11 goals from 14 Serie A games in the 2021-22 season, including six from his last four in the top flight. body check tags ::