The defender has settled well in the Italian capital since he arrived on loan last summer and Fonseca said that Smalling wants to stay at the Italian club beyond this season, with his loan deal set to expire at the end of the campaign. Sources have told ESPN that while a deal has yet been agreed to make his move permanent, Roma are confident it can be done.
"I will do everything I can to keep him at Roma next year too," Fonseca said. "I know he wants to stay, let's see what happens.
"He's an amazing man, so humble, so professional. He is adored by the fans and established himself as one of the leaders in the dressing room.
"It's not easy for English central defenders to adapt so quickly to Italian football, the record there isn't good. But he has been amazing."
Smalling missed Roma's opening four games this season but has been a first-team regular ever since, starting 21 of the next 22 Serie A games.
The 30-year-old, who joined United from Fulham in 2010, has two years left on his contract at Old Trafford.
Meanwhile, Fonseca tipped midfielder Nicolo Zaniolo to become one of the best players in Europe if he continues to improve.
Zaniolo, who arrived from Inter in the summer of 2018 as a make-weight in the deal that took Radja Nainggolan to the San Siro, suffered a season-ending cruciate ligament injury in January that will keep him sidelined until late-Autumn at the earliest.
The 20-year-old had established himself as one of the most promising youngsters in Serie A this season. He won his first caps for Italy last year, as well as earning calls to be a starter at the now-postponed Euro 2020.
"He's not just a wonderful natural talent, he's a player who improved considerably this year," Fonseca added. "I used to say he was like a wild man, following his instincts, but now he understands the game, understands the space, understands the decision-making.
"I have no doubt that in a few years he'll be one of the best players not just in Italy but in all of Europe."