Montella is the favourite to replace Luis Enrique after the Spaniard announced last week he would not continue in charge despite having one year left on his contract.
Reports in Rome claim the Eternal City giants are willing to offer Montella a two-year deal with an optional third year.
"I would be delighted if Montella returned," De Rossi said. "I always thought he was a good coach and his experience in Catania has confirmed that."
Montella guided Roma to end sixth in Serie A in the 2010/11 season, having taken over as caretaker boss in the February, but was not offered a contract extension to remain at the Stadio Olimpico.
He joined Catania last summer and led them to a respectable 11th-placed finish this season, while Roma finished outside of the European places in seventh.