The Blues were strongly linked with the right-back after Inter Milan president Massimo Moratti admitted the player's future was in the balance.
But Maicon's representative, Antonio Caliendo, has revealed big-spending City and Madrid have also entered the race.
Caliendo said: "Maicon is the best right-back in the world.
"Real are interested and I think Manchester City too.
"However, it is up to Moratti to decide. I would be happy if Maicon stayed at the San Siro to try and win the Champions League."
Moratti recently claimed it was only 50-50 as to whether Maicon, 27, would still be at Inter next season.
But Caliendo insists the speculation has nothing to do with his client's lifestyle.
He added: "For all I know Maicon is tied to Inter for the next four years.
"But this is football nowadays, things change very rapidly. Everybody can be sold or bought.
"He is a serious professional and not a party animal like they describe him in Spain."