The 30-year-old has spent the last eight years with the Serie A outfit but he will soon be entering the final year of his contract.
Koulibaly's agent is believed to have been pushing for his client to move to either Barca and Chelsea, who have identified the centre-back as a potential target this summer.
However Spalletti has played down talks that the Senegal international with seek pastures new, telling Football Italia: "Koulibaly in my view is not for sale, just like last season when I threatened to chain myself to the gates if he was sold. I'm doing it again!
"This is a player always open to giving a helping hand, knows where to intervene and how to raise the level, he does what is needed. We want to have another important season, so he cannot be sold.
"People say you can get a younger player, but you can't buy a leader, who developed here over so many years, who lives and breathes the city and gives that passion back on the pitch. Kalidou is not the same as the others for many reasons, so he needs particular focus. These are all things we'll discuss over the next few days."
Koulibaly, who is allegedly valued at around €35m (£29.6m), made 34 appearances for Napoli across all competitions in 2021-22, scoring three goals and providing three assists.