That sounds a lot like Inter management leaking "information" to media, to make themselves look better. At least it won't bother them even if they deny it and publicly show their support to the coach.
Idea is to set the narrative well beforehand, so when the sacking time comes, it all makes sense to just sack the coach. Only one scapegoat, who takes the blame.
And interestingly indeed, Correa didn't want to leave so it's a moot point. With Sanchez, it was possibly for us to "force" him out by just buying out his contract, with Correa that wasn't possible.
And, to make myself clear, I'm pretty sure sacking Inzaghi is our only option to save the season. But the reason for that is not this low-level BS media is running around but the cruel fact we cannot change our management or ownership to make any difference now and we cannot change our squad middle of the season. Only role which can make a difference from current situation is the coach and that's why he will get fired eventually.
But that will make also the management and the owner look a bit silly so they want to cover their asses. And the public narrative against the coach is perfect for them while in reality it all starts from the owner and comes down to the management and only then to the coach + players.