The England defender and Armenian midfielder have impressed during loan spells at Stadio Olimpico, and could be set to stay in Italy beyond the summer
Smalling and Mkhitaryan are currently taking in season-long loan spells at Stadio Olimpico from Premier League duo Manchester United and Arsenal respectively.
United centre-back Smalling has earned plenty of praise for his performances for Roma, who are determined to make the England international’s deal a permanent one in the Italian capital.
Smalling has featured in 26 matches across all competitions for the Giallarossi, contributing two goals and an assist.
“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, a former United team-mate of Smalling, has experienced an injury-interrupted spell with Roma.
However, the attacking midfielder has still managed five Serie A goals and a pair of assists after scoring and creating another in the 4-0 rout of Lecce on Sunday.
“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.”
Smalling and Mkhitaryan will be back in contention for a place in Fonseca’s starting XI when Roma take on Gent in a Europa League round of 32 second-leg tie in Belgium on Thursday, where they will be defending a 1-0 lead from the reverse fixture.