According to Calciomercato, an initial €30m offer was submitted for the Croatian global but was rejected, and in turn the new bid has come in and the Nerazzurri have given him the green light to complete a move to United.
Inter are reluctant to let Perisic leave but club chiefs hope a windfall from United will offset FFP concerns.
Perisic famously fell out with Jurgen Klopp when he worked under the German at Borussia Dortmund, with the tactician now in charge at Liverpool accusing the Croatian of being "childish" as he off-loaded him to Wolfsburg.
Mourinho is still confident that Perisic fits the bill at Old Trafford, however.More news: Novak Djokovic enters 3rd round of French Open
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Although the season has been a disappointing one for Inter, finishing seventh in Serie A, it has been another impressive campaign for the Croatian.
The potential breakthrough in the Perisic deal comes as United re-assess their transfer options after "cooling" their interest in Atletico Madrid striker Antoine Griezmann.
The decision to uphold Atletico Madrid's transfer ban has meant that the France global is staying in Spain, which forces United to focus on other targets.
Nevertheless, the report goes on to add that negotiations between the two parties started back in March when Mourinho travelled to Zagreb to meet with his agents while it's claimed that Perisic will earn over €5m-a-season, double what he's earning now.