Roma are hoping to sign on-loan duo Chris Smalling and Henrikh Mkhitaryan to permanent deals at the end of the season.
Speaking to Sky Sports News, Fonseca said: "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. I would also like to keep Mkhi in our team."
Roma now sit fifth in the Serie A table and they continue their Europa League campaign on Thursday when they travel to take on Gent in Belgium.