Media reports in England have suggested that Manchester City are looking at the Paraguayan following the departure of Carlos Tevez to Juventus.
The 30-year-old scored 26 goals in all competitions last season for Benfica, who finished as runners-up to FC Porto in the Portuguese Primeira Liga.
However Cardozo is thought to have fallen out with Benfica coach Jorge Jesus and he could be set to leave the Estadio da Luz.
New City manager Manuel Pellegrini will want to add a striker to his ranks, and reports claim Cardozo could cost in the region of €20m (£17.1m).
"Benfica knows the situation and now the subject is in their hands," Cardozo's agent, Pedro Aldave, told Sky Sports.
"There has always been interest from Premier League but now this is real interest."
Bayern Munich's Mario Gomez is also reported to be on City's radar, along with Alvaro Negredo of Sevilla and Roma's Pablo Osvaldo.
City have bolstered their squad with the additions of midfielder Fernandinho from Shaktar Donetsk and winger Jesus Navas from Sevilla since the dismissal of Roberto Mancini at the end of their unsuccessful Premier League title defence last season.