The grandparents of a missing four-year-old boy say they are “absolutely devastated” after a family member was declared a suspect in his likely death.

Gus Lamont was last seen by his grandmother playing at the homestead of a sprawling sheep station in outback South Australia on September 27.

Police on Thursday declared his disappearance a major crime, saying they had a suspect who lived at Oak Park Station.

They confirmed the boy’s grandparents, his mother and his younger brother were at the property at the time he disappeared but stressed his parents were not suspects.

Gus’s grandparents Josie and Shannon Murray released a brief statement via their lawyers, Andrew Ey and Casey Isaacs respectively, on Friday.

“We are absolutely devastated by the media release of SAPOL Major Crime,” it read, referring to the South Australian Police update.

“The family has co-operated fully with the investigation and want nothing more than to find Gus and reunite him with his mum and dad.”

Their lawyers told AAP the couple would not comment further.

Detective Superintendent Darren Fielke said on Thursday a person who lived at Oak Park Station had withdrawn co-operation with the investigation after “a number of inconsistencies and discrepancies” were identified in the information they provided.

Gus’s disappearance sparked intensive searches spanning almost 500sq km and involving hundreds of police and volunteers using aerial support and mounted units.

Fielke said initial searches were based on Gus walking off the station and becoming lost but the case was now a major crime.

The two other investigation options were focused on Gus being abducted or whether someone known to him was involved in his disappearance and suspected death.

“We don’t believe now that Gus is alive,” Fielke said.

Investigators searched the homestead on January 14 and 15, seizing items including a vehicle, a motorcycle and electronic devices for forensic testing.

Fielke said ground and aerial searches failed to locate Gus or any items belonging to him and family members had provided information that police had reviewed.

“As a result of that, we have identified a number of inconsistencies and discrepancies with that information as it relates to timelines and the version of events provided to us by the family members,” he said.

“It’s challenging, it’s delicate at times when you’re dealing with family members … our people have been unwavering and kept an open mind.”