The Croatian is out of contract in June, and with an extension to his existing deal yet to be agreed with the Serie A club, he is free to move teams at the end of the season.
Thomas Tuchel's side have made their move according to Sport Mediaset, with the Londoners having agreed a deal subject to a medical and the formalities being signed off.
After scoring two goals in Inter's 4-2 win over Juventus in the Coppa Italia on Wednesday evening, Perisic criticised the club when speaking to the outlet.
"I don't know anything yet. With important players, you don't wait to the last minute. You ought to know that too," the 33-year-old told Sport Mediaset.
Primarily playing as a winger, but also being utilised as a wing-back on numerous occasions, Perisic has scored seven goals and registered six assists in Serie A so far this season, helping Inter to challenge for the Scudetto with rivals AC Milan.
Having joined the club for around £17m in 2015, Perisic has enjoyed a successful spell in Italy, and was part of last season's side that won the title under Antonio Conte. body check tags ::