Conte has cast doubt on his future with the Nerazzurri after last night's Europa League final defeat.
He said, "If some situations end up affecting my family, that is no longer enough for me. Everything has its limits, I have to see where my limits are.
"We'll clarify the situation, without rancour, because I will always be grateful for having the chance to spent a great year at Inter, but on the other it was also very tough."
Conte confirmed he will not resign from his role but that could not be enough to keep him in the role.
He claimed: "If you think I will step back, I won't. I said what I think, you heard my words and they have not changed.
"Something happened, there's no point beating around the bush. We have to see whether everyone is prepared to not have another year like this for what happened with me.
"There are a few situations I will evaluate, it's only right the President evaluates it too, I'll tell the directors my views.
"Beppe Marotta, Piero Ausilio, they were all convinced I should come here and I will always thank them."