Perisic has been the centre of ongoing speculation linking him with a move to Premier League giants United.
The 28-year-old Croatia international winger, however, is set to stay in Milan according to Spalletti.
"Perisic is determined to remain," Spalletti said via Sky Sports Italia following Inter's 1-0 friendly win over Real Betis.
"He spoke like a player who wants to do well and be professional."
Spalletti spoke less favourably about want-away Inter midfielder Geoffrey Kondogbia.
"Kondogbia has been very disappointing and his behaviour does not reflect the person we know. He is damaging himself with this behaviour," Spalletti said.
"He wants to go to Valencia on loan and save a bit on his wages, but he wants it too easy… When there is something you don't agree on, you find a middle ground. Considering the money spent on him, it's difficult.
"In my view, Kondogbia was given some bad advice, as this sort of attitude is just not part of his personality.
"Kondogbia is strong and has been paid as a strong player, so if there aren't the right conditions for him to go, then he's staying here. We'll evaluate whether to sign someone else in the middle, but I won't let a quality player leave without a quality replacement."