The 28-year-old has been very much part of the Serie A club's plans, after making 31 appearances last term, but Perugia are bracing themselves for a concrete bid for the Brazilian.
After making his name with Palmeiras and Parma, Ze Maria has caught the attention of Valencia and Atalanta in the past, but Deportivo and Chelsea are believed to be the latest clubs in the frame.
Blues boss Claudio Ranieri may view the South American as an alternative to Real Madrid's Geremi Njitap, should his bid for the Cameroon international continue to stall, with the Liga champions demanding a sizeable fee for the African.
Geremi remains Ranieri's top target but other options are now being assessed, due to the current impasse reached with Real.
Deportivo are also interested, as their full back Manuel Pablo continues to be targeted by Real Madrid, and Ze Maria could find himself very much in demand.
Meanwhile, Deportivo have agreed to allow keeper Petr Kouba to move to his native Czech Republic with FK Jablonec.
