Perisic scored one and set up the other as Croatia came from behind to beat England in extra time on Wednesday and reach their first ever World Cup final.
Rumours linking the 29-year-old with a move to Old Trafford have been circulating for the best part of a year now, but according to Paris United (via Get French Football News) these talks are now at a more advanced stage than ever before.
Perisic's representatives Fali Ramadani and Pini Zahavi are said to be travelling to Manchester to finalise the formalities before Perisic can complete the details of the transfer after his involvement in Sunday's final.
Jose Mourinho has not disguised his admiration for Perisic and he was singing his praises again as part of his punditry work for Russia Today during the match against England.
"Perisic is the kind of winger that is different to the others," the Sun quotes Mourinho as saying.
"Normally you look at wingers and they are just fast and creative but he is also physical, very physical, fantastic in the air."
Reports last summer claimed that United had agreed a £40m deal to sign Perisic before Inter upped his value to £50m at the eleventh hour.
Their valuation is unlikely to have decreased after a season in which the Croatian scored 11 goals and helped Inter return to the Champions League for the first time since 2011/12.
Perisic has featured in every game Croatia have played at the 2018 World Cup. They face France in the final this weekend.