The 33-year-old has decided to remain at the San Siro club where he has been a player since 1999 after moving from Salernitana.
"I evaluated the offer," Gattuso told Gazzetta dello Sport.
"It was an important offer but in the end, I believe it is better to be with the family at home.
"I have been 12 years at Milan and it's my home."
The Italian made 31 league appearances this season to help Milan clinch the Scudetto for the first time since 2004.
