The striker has thrived under Stramaccioni since moving from AC Milan in the summer.
The coach remarked: "Calling it friendship is perhaps a bit excessive but I have been very open with him, since before he even became an Inter player. What we have in common is the fact that we both came from nothing, and I don't mean to disrespect my or his origins by that, but we speak very openly and I think that's one of the reasons why we understood each other immediately.
"His importance on the pitch is unquestionable. I think the excellent relationship he has with his wife and the coming birth of his second child Christopher have helped him to mature. I'm holding onto Antonio tight, I think he's already proved that he's an extra resource for Inter, like all the quality players were already here."