The 22-year-old has been in prolific form for Jorge Jesus's side in the early stages of the season and found the back of the net twice against Barcelona in the Champions League in midweek.
Nunez was previously linked with moves to a host of top European outfits before arriving at Benfica from Almeria last summer, and his days in the Primeira Liga could supposedly be numbered.
The report adds that City's previous dealings with Benfica - striking transfers for Ederson and Ruben Dias - will help them when it comes to negotiating with a side who they enjoy a strong relationship with.
The English champions are reportedly hopeful of driving Benfica's asking price down to £70m for Nunez, who boasts 20 goals and 12 assists from 51 games for the Portuguese giants. body check tags ::