Perisic was a top target for Jose Mourinho this summer but a switch to Manchester United now appears unlikely.
The Croatian winger will increase his salary to €5.5m-a-year at the San Siro, Transfer Market Web report.
That works out at roughly £96,000-a-week.
Mourinho has made three signings this summer but wanted four.
Victor Lindelof was recruited from Benfica to strengthen at the back with Romelu Lukaku drafted in to lead the line.
Nemanja Matic arrived from Chelsea for £40m to be a rock in midfield but adding a winger was also on the United manager’s mind.
“Man Utd target Ivan Perisic is close to signing a new Inter Milan contract”
He may now have to settle for just three three additions, although Zlatan Ibrahimovic is likely to join to bolster the frontline.
Starsport revealed yesterday that Zlatan will accept a huge pay cut to return to Old Trafford.
He earned around £300,000-a-week last season, but could sign for just £125,000 now.
Ibrahimovic’s contract wasn’t renewed after he injured his knee against Anderlecht in April.
It means he’s a free agent and can sign for the club at any time, and isn’t bound by the transfer window.