Gattuso and striker Inzaghi - who played in the 2-1 win over Liverpool in 2007 with Inzaghi scoring twice - held talks with Milan president Adriano Galliani on Friday before announcing their departure from the club.
Former Rangers midfielder Gattuso has suggested he may be forced to quit the game with a rare eye condition.
“Tomorrow we will hold a press conference at Milanello,” said Gattuso
“I'll take a year out, this is goodbye and we’ll see what happens in the coming year. I have nothing on the table at the moment.
“I’ve missed a year with injury and I have realised that now there is no space for me here, so it’s time to make way for players that are younger than me.
“I will meet again with Milan in the next year, but not as a player.”
Inzaghi, now 38, penned a farewell letter to fans. He is expected to continue his career elsewhere after being stuck on the fringes during his final season with the club.
“The first and only thing I want you to know forever is this - I have played and won for us,” he said.
“To play and win without sharing emotions is nothing, but you and I, us, we did everything together.
“We hoped, we suffered, we cheered, we celebrated. We lifted cups and titles together with our hearts. We were always on the same wavelength. And no-one can ever take this away.”
Former Italy defender Alessandro Nesta has already departed Milan for a possible move to the USA.