It is reported in Spain that Espanyol met with Zabaleta's agents this week and agreed that they have until 1st August to find him a new club.
Zabaleta wants a move to Italy or England and City are the first to show an interest in the Argentine international.
The 23-year-old is currently under contract for another two-years with Espanyol but they are ready to talk terms.
However, Espanyol want £15million for Zabaleta.
Sporting director Paco Herrera says the club are yet to receive any firm offers for Zabaleta.
"There are many rumours about our players, but we have not received an offer," he said.