Last month, Pellegrini was appointed as the new boss of the Hammers and the East London outfit have indicated that they will go on a 'record-breaking spending spree' ahead of next season.
However, Pellegrini has claimed that West Ham are unable to afford Chilean compatriot Bravo, who may be allowed to leave the Etihad Stadium.
While acknowledging that City previously failed with bids for Alexis Sanchez and Arturo Vidal, the 64-year-old told Encuentro El Mercurio: "I would happily take them to my team, but now for economic reasons, it is impossible. Signing Bravo for West Ham is not viable either."
Pellegrini is in the market for at least one goalkeeper, with Joe Hart having returned to Man City after a season-long loan spell.