Smalling has made 26 appearances in all competitions for Roma this season and revealed earlier this week he is open to extending his stay in the Italian capital beyond the end of the season.
As it stands, Smalling is scheduled to return to parent club Manchester United at the end of the season but Fonseca is desperate to hang on to the 30-year-old defender.
“Chris is a great, great man, a great, great professional,” Fonseca said .
“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.”