Italy have drawn Northern Ireland in the semifinals to be staged in March.
Liverpool attacker Chiesa declined selection for the final round of group qualifiers this past week.
And when asked about the player's status, Gattuso stated: "You know this very well.
"You always ask the same questions. I call Chiesa. I call him before every international break.
"The problem isn't Gattuso or his coaching staff. It's his problem. Not ours. You know that very well. You always ask me the same questions and I keep giving you the same answer."
He also said: "I often talk to him. We have to respect the decisions and problems that each of us has.
"We know well what we tell each other, and I must respect what the player tells me. I can't say anything else."
Asked if the decision had come from Chiesa himself, Gattuso replied: "Yes, it's already the fourth or fifth time that I'm explaining this."