The 36-year-old left PSG at the end of his contract this summer before being named as player of the tournament at the Copa America as he captained Brazil to glory.
Pep Guardiola has been linked with a swoop for the right-back, who he worked with during his time as Barcelona coach.
However, El Mundo Deportivo reports that City face competition from Premier League rivals Arsenal and Spurs for the veteran defender.
Unai Emery has asked the Gunners’ hierarchy to make Alves an offer, while Tottenham have made contact with the player’s representatives.
The Brazilian is set to be keen on continuing to play in Europe, but has also received offers from further afield.