The 29-year-old Roma midfielder is a long-term target for Roberto Mancini, who has been trying for months to lure him to England, before turning down a move to the Etihad Stadium during the summer.
De Rossi was a surprise guest at Manchester City's 0-0 draw with Chelsea at Stamford Bridge on Sunday, and according to reports he and his wife Sarah held talks with the reigning Premier League champions about a transfer in January.
With 82 caps for Italy, the playmaker is currently the best-paid player in all of Serie A, but is eager to win trophies following five second-place league finishes with Roma.
Mancini is keen to further bolster his midfield, with summer signings Jack Rodwell and Javi Garcia failing to impress at City this season, and know that Roma require funds to rebuild their team.
"If we were to get another offer from them we would listen again."
Chelsea showed interest in De Rossi before Roberto Di Matteo's sacking as manager last week, but City are very much in pole position to sign him, as the veteran's ongoing feud with Roma coach Zdenek Zeman continues.