Roma are hoping to sign on-loan duo Chris Smalling and Henrikh Mkhitaryan to permanent deals at the end of the season.
30-year-old central defender Smalling joined the Italian giants from Manchester United and he has since made 26 appearances in all competitions for Paulo Fonseca's side.
Armenian international Mkhitaryan has been hampered by niggling injuries since making the move from Arsenal but he got a goal and an assist in Roma's 4-0 win over Lecce on Sunday.
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.