Mancini so far enjoys a 100 per cent record as City manager since succeeding Mark Hughes.
"I did receive four or five offers, but I preferred to wait. There was a bit of a discussion with an Italian club and I never got too deep into it. The rumours about Juventus were totally untrue. The others were all foreign," he told Sky Sport Italia.
"I think Manchester City can have a great future and they chose me. I accepted because it seems like an interesting challenge.
"I don't think we can win the title, but if we can do well then we could finish in the top four. It isn't easy to target the Champions League, but sooner or later we'll get there. The club has real prospects and can be among the best in the world relatively quickly."