Starsport understand United have been negotiating with Inter for Perisic since the end of last season.
He was a good player in the Bundesliga, but really elevated himself last season and seems more than ready for a top club.
The Inter boss doesn't state what their valuation is but the Mirror claim the Serie A outfit are holding out for a fee in the region of £50m for the 28-year-old winger.
Spalletti told a media conference: "He is a fantastic player and if his future is totally up to me, I will definitely keep him".
Perisic is now with Inter on their preseason tour of China and played 45 minutes of the 1-1 draw against Schalke on Friday.More news: At least five injured in horror 'chainsaw attack'
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United have already brought in Victor Lindelof from Benfica and Romelu Lukaku from Everton, spending over £100m on the pair.
His blue-collar approach and high work rate would make him a ideal fit for Mourinho's philosophy, and United have the kind of financial might to overpay if they have to.
Should United get a deal for Perisic over the line, it'll be interesting to see whether the winger can displace current United first-team player Anthony Martial and cement his place in Jose Mourinho's United starting line-up.
Perisic is still a player Mourinho is very keen on, and he is putting pressure on Woodward to deliver the signings he wants.
He has little room left for growth, however, and £50 million is a lot of money for a 28-year-old who is a good, but not a world-class option.