De Rossi stated publicly earlier this week that he wants to stay with Roma, but Mancini still thinks there is a deal to be done.
He said: "I don't know this. It is difficult but I don't know what can happen.
"From my experience while the window is still open anything can still happen for every player."
Mancini also confirmed that midfielder Nigel de Jong will stay at the Etihad this summer.
City play their first away match in the defence of their Premier League title away to Liverpool on Sunday.