Police sources told Indo-Asian News Service the bribe was offered so the family would not register a first information report in the case.
The name of the police officer has not been released.
The 5-year-old girl was abducted April 15 and held hostage for two days in a ground floor apartment in the east Delhi building where her family lived.
Authorities said she was sexually assaulted and brutalized before being rescued after members of her family heard her screams.
The child is being treated at the All India Institute of Medical Sciences.