The Roma midfielder has long been linked with a move to the Premier League champions, who reportedly enquired about the dynamic midfielder earlier this summer.
However, Roma have continued to insist that they will not sell De Rossi for now, but Giorgio De Giorgis says that that stance may not stop Mancini from making yet another approach.
"I can confirm the interest in De Rossi," he told Tele Radio Stereo.
"Mancini really likes De Rossi and an offer could be up to the task, seeing as so far Manchester City haven't done much on the transfer market.
"Roma consider the player to be unsellable, but I don't know if De Rossi's agent Sergio Berti really is in Manchester, as the media have claimed."
City will begin their Premier League campaign with a home game against Southampton on Sunday.