The England international was unveiled by the Serie A side on Friday after arriving on a season-long loan deal from United a week earlier.
But he is already considering extending his stay on the peninsula as he settles into life at his new club.
“I’m very eager to come. It happened very quickly,” he said at a press conference.
“I’m focused on the next game, getting up to speed with the manager’s methods. Then I’ll see what happens next season.
"If it prolongs and everyone’s happy, I could definitely see a long-term future in Italy.”
Smalling was also asked for his thoughts on the racist abuse directed at his former United team-mate Romelu Lukaku, who is now at Inter Milan, by Cagliari fans over the weekend.
A section of the home support directed monkey chants at the Belgian, before an Inter Ultras group made matters worse by defending the actions of those responsible in an open letter to Lukaku.
“I think racism is unacceptable and shouldn’t be stood for,” Smalling said.
“But it’s not an issue just in Italy, it’s around the world. There needs to be a change, a generational change, to make people not act like that.
“It’s a world issue and happens everywhere, but it’s very sad it happens in these modern times.”
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