The Daily Express says City want Maicon - and are willing to offer Elano and Â£10million in cash.
And the 27-year-old Maicon, above, who had a superb season as Inter clinched a third Serie A title on the trot, is his top target, although he faces competition from Real Madrid and Chelsea if Inter decide to sell.
Agent Antonio Caliendo said: "Maicon is the best right-back in the world. I can rule out that Manchester United are interested but City have made an approach."
Midfielder Elano, who cost City Â£8m two years ago, has stated his desire to join Inter and fallen further down City's midfield pecking order after Barry's arrival.