Zarate admits he's happy with his first weeks at Inter.
He said: "I did quite well in my first year at Lazio but my second season wasn't good, it was a bad year. Then last season, my third, we came within a whisker of achieving our aim of getting into the Champions League.
"I scored some goals last term but it was quite a normal year. Now I feel I have matured and I hope this will be a huge season for me.
"I'm very happy in Milan, I really like it here. Rome is a beautiful city but it's more chaotic. Milan is calmer, I like it.
"It's true that there were some English clubs after me but Inter are Inter; I had no doubts about where I wanted to be.
"Beppe [Bozzo, his agent] said to me: 'Come up to Milan because we have to speak to Inter.' So I set off immediately unaware that it was nearly all wrapped up.
"He knew it was already a done deal but I didn't, so I was really tense. On the plane I was even in a cold sweat.
"I was so happy that day. And now I want to remain here at Inter. Of course I'd like to stay here. That's what I want and what I really hope I do."