Perisic will be out of contract at Inter in the summer and he has been left annoyed by what he sees as the club taking too much time to put terms on the table for him.
Inter are expected to offer him a new two-year contract but there are suggestions that the Croatian could leave on a free transfer.
Newcastle have reportedly offered him lucrative terms, but there are question marks over whether he would agree to join the Magpies.
But it has been claimed that he is very close to agreeing on a deal to move to the Premier League with Chelsea.
Chelsea have already agreed personal terms on a contract with Perisic, according to Italian journalist Sandro Sabatini, cited by CalcioMercato.it
It is suggested that Perisic is now on the verge of making the move to Stamford Bridge.
Inter are still hopeful of him signing a new two-year contract and staying at the San Siro next season.
