The Croatian forward was on loan at Bayern Munich last season, helping the team to win the UEFA Champions League.
Bayern did not sign him permanently, while Inter are happy to cash in on the 31-year-old.
Per Fussball Transfers, United, Everton and Leicester all intend to inquire about Perisic in the coming weeks.
It is unclear who will make the biggest offer, or whether one of the clubs may want to take him on loan for the season.
Inter reportedly want €15 million for Perisic.