The Croatian midfielder is reportedly being chased by incoming manager Antonio Conte.
The 27-year-old joined the Milan club last summer from Bundesliga side Wolfsburg in a deal worth £12.5 million.
Reports state Italy national team head coach Antonio Conte is eager to bring the Croat to Stamford Bridge following the conclusion of his duties at Euro 2016.
In spite of the considerable speculation, Perisi - who has made 32 league appearances for the Nerazzurri scoring 6 goals - has made it clear he would be open to remain at the San Siro for the foreseeable future, acknowledging the grand history of the Serie A giants.
As quoted in the Daily Star, he reportedly said: “Inter is a big step in my career. They're a big club and I'll do my best to perform well here.
"I really like Italy and Inter. When I was a kid I used to watch several leagues and I knew the names of all the greats that have played for this club. Italy is a gorgeous country and I really like it.”