The body of 42-year-old Peter Ritchie was discovered in woods at Kippen, Stirlingshire on Monday.
The Daily Record reported that police were told about the car on Sunday night but could not find it.
The vehicle and Mr Ritchie's body were discovered by police the following day.
Police said Mr Ritchie's death was being treated as unexplained.
A statement issued by Mr Ritchie's family said: "Peter was a much loved son and brother and as a family, we have been left devastated by his death.
"It will take time to come to terms with this loss and as such, we would ask for our privacy to be respected so that we can grieve in peace."
Circumstances investigated
The Crown Office and Procurator Fiscal Service (COPFS) has now instructed the Police Investigations and Review Commissioner (Pirc) to investigate the circumstances leading up to the discovery of Mr Ritchie's body and the vehicle.
A Pirc spokesman said: "The investigation will focus on the actions of Police Scotland when responding to telephone calls made by members of the public and family on Sunday 29 January and Monday 30 January.
"A report on the Commissioner's findings will be submitted to the COPFS in due course."
A Police Scotland spokeswoman said: "Police in Stirlingshire are investigating following the death of a man in a wooded area near to Woodstone Road, Kippen.
"The body was discovered in the area around 22:45 on Monday, 30 January.
"The death is currently being treated as unexplained and inquiries are currently ongoing to establish the full circumstances."
A police watchdog investigation has been launched after a missing man was found dead near his abandoned car a day after officers reportedly looked for the vehicle.