The Premier League champions were rumoured to have been chasing the Italian international last summer, but a deal could not be reached with his club.
City instead signed Jack Rodwell and Javi Garcia, but the duo have failed to live up to the expectations at the Etihad Stadium.
This has led to speculation that Roberto Mancini could return with another bid during the next transfer window, as he looks to rebuild his squad after an underwhelming campaign.
However, his pursuit could be thwarted by either Real or PSG, with the mega-rich pair keen on snapping up De Rossi.
The Spaniards are believed to be in the market for midfield reinforcements, whilst the Parisians are looking to lure top players to the club as they attempt to become a world footballing superpower.
De Rossi is widely regarded as one of the best central players in Italy, and has always been thought of as a one-club man, having graduated from Roma’s academy.
But, the 29-year-old is thought to be unsettled at the Stadio Olimpico, with the Roman outfit struggling to challenge for Champions League qualification and major honours.