Koulibaly has been strongly linked with Premier League giants Manchester City and Ligue 1 champions Paris Saint-Germain as Napoli look to raise funds following the club-record signing of Victor Osimhen.
The 29-year-old Koulibaly played as Napoli opened their 2020-21 Serie A season with a 2-0 win at Parma on Sunday and Gattuso hailed the in-demand centre-back, who has also reportedly attracted interest from Manchester United.
"I had no doubts, he is one of the strongest champions in the world in his role," Gattuso said via Sky Sport.
"He has always given me great availability and always trains well. I would be sorry to lose him, both for the man and for the player.
"But you know that numbers are important for clubs and at this moment something needs to be done for numbers, but I'd be happy to keep him."
Osimhen made his debut for Napoli, coming off the bench to inspire the visitors as Dries Mertens and captain Lorenzo Insigne scored against Parma.
When asked about the Nigeria star, Gattuso added: "It's not about numbers, but the principles of football. We know Osimhen is an added bonus, but we need to run before we have quality, because quality is not enough on its own.
"We must set out the team with the right concepts and protect the defence, but we knew that Osimhen could give us another gear in the final 20-25 minutes today.
"Osimhen is a lad who, in the 25 days I've been working with, I can tell doesn't forget where he started from, who made sacrifices, lost his family very young and has the head of a 40-year-old on 21-year-old shoulders.
"I am confident he won't change, as he has a great attitude and at this moment is a better player than he's so far shown on the pitch."
Osimhen scored six goals across his first two pre-season games for Napoli and will be hoping to find the back of the net in his club's next Serie A match against Genoa on Sunday.