The Manchester United stopper has impressed while on loan in the Italian capital this season, making 21 appearances and scoring twice.
United want at least £25m for the 30-year-old, and Fonseca hopes a deal can be negotiated.
"He surprised me. He's a defender that had never left England and he arrived in a league very demanding of tactics, where details make the difference," the Portuguese boss told A Bola.
"Chris adapted very quickly. He's an extraordinary guy, very intelligent. He has characteristics that I really appreciate in the centre.
"He's fast, nearly unbeatable in one-on-ones. He has a great ability to read the play and anticipate. He was very important for this club.
"If possible, I would like him to stay. He's a great professional and person, it's a pleasure to have him here with us."