De Rossi has yet to extend his contract with the Serie A outfit, with his current deal ending next summer.
Mancini reportedly described the 28 year old as "absolutely perfect" for his club although he too expects the midfielder to remain in Rome next season.
"Daniele's contract expires next year and he is in negotiations to extend it," said Luis Enrique.
"He wants to remain and the club wants to keep him and I can only speak highly of him.
"The two sides must find an agreement."