Perisic will be out of contract at the end of next month and Inter have been interested in holding on to the player.
The Nerazzurri have offered him a new deal but the Croatian is unhappy about the terms on offer from the Serie A giants.
Inter do not want to offer more money to a 33-year-old and it has been claimed that he could now be on his way to the Premier League.
Antonio Conte is a firm fan of the player who he turned into a wing-back when they were together at Inter.
With Perisic considering leaving Inter, Spurs are now leading the race to sign the player on a free transfer this summer.
And there is increasing confidence at Tottenham that a deal can be done to take Perisic to north London.
He is the kind of experienced player Conte is looking for as he can slot straight into the Spurs team next season.
