Smalling and Mkhitaryan moved to the Italian capital on season-long loan deals from Manchester United and Arsenal respectively at the start of the campaign.
The pair were instrumental as the Giallorossi snapped a three-game losing streak by beating Lecce 4-0 at the Stadio Olympico in Serie A on Sunday.
Smalling revealed in an interview with the BBC last week that moving to Italy has made him a better player and would like to extend his stay at AS Roma, where he has made 26 appearances in all competitions.
"Chris is a great, great man, a great, great professional," Fonseca told Sky Sports News.
"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."
Mkhitaryan has had a comparatively difficult time with injuries since making the switch from North London but has impressed when called upon.
The Armenian has scored five goals in 15 games for Roma which has caught the eye of his manager.
"Mkhi during this season got some injuries but he is returning now and he is proving his quality," Fonseca said.
"Let's see. He is a player with great decisions on the pitch and I would also like to keep Mkhi in our team."
