England international Smalling, 30, joined the Giallorossi on a season-long loan in late August, but it's understood the €3 million temporary deal had no option for a permanent transfer included.
"Chris is a great, great man, a great, great professional. The adaptation (to Italian football) was very easy for him. He's a boy that everyone loves in the club because he is a great professional.
"I would like Chris to stay. We are speaking. I don't know if it is possible because of the situation with Manchester United, but I would like so much for Chris to stay here with us because he is very important.
"He is a great player, a great man with a great attitude every day and for all of these reasons I would be very happy if Chris stays."
The former Porto and Shakhtar Donetsk coach was evidently impressed after Roma kept a second clean sheet in four days having beaten Gent 1-0 in their UEFA Europa League round-of-32 first leg on Thursday.
Mkhitaryan looked back to his best at the Stadio Olimpico on Sunday when he scored and assisted in Roma's second successive win across all competitions:
The Armenia captain joined Roma on loan from the Gunners on September 2—also for €3 million, plus a potential €100,000 in bonuses—though injury setbacks have limited his involvement thus far.
Fonseca added: "Mkhi during this season got some injuries but he is returning now and he is proving his quality. Let's see. He is a player with great decisions on the pitch and I would also like to keep Mkhi in our team."
Roma have kept back-to-back clean sheets for the first time since late November, and Smalling has played the full 90 minutes in all but one of their 21 league matches since making his Serie A debut in September.
United manager Ole Gunnar Solskjaer might consider allowing the player a move given the centre-back competition at Old Trafford. The club signed Harry Maguire from Leicester City last summer, while Eric Bailly, Victor Lindelof, Phil Jones and Axel Tuanzebe have also been in the rotation this season.
Solskjaer seemed certain in his response when asked in December whether he thought Smalling—who has made 323 appearances for United—would return to the club, per broadcaster Bill Rice:
Arsenal have changed manager since Unai Emery agreed to send Mkhitaryan to Rome, and incumbent boss Mikel Arteta may yet want to give the player a chance in north London.
However, sportswriter Jonny Singer appeared to suggest the playmaker hasn't made the necessary improvements to warrant another chance at the Emirates Stadium:
Mkhitaryan, 31, has never recaptured the superb form he enjoyed at former clubs Shakhtar and Borussia Dortmund. He endured a disappointing 18 months at United before he was traded for Alexis Sanchez and sent to Arsenal in January 2018.
A permanent move to the Italian capital could make sense for him and team-mate Smalling, each of whom hope to help Roma—currently fifth in Serie A—to a top-four finish before their loans come to an end.