SA Police will speak to the media at 1pm local time (1.30pm AEDT) to provide an update on the case.
A full-scale ground and air search of the property and surrounding area was launched after Gus went missing.
A three-day search of six mine shafts near Oak Park Station also failed to uncover any evidence.
Police received more than 150 Crime Stoppers tips about the missing boy.
“We’ve taken statements with the family, we’ve had to go through those statements with the family, and that’s just part of the normal investigational process that we go through,” Detective Superintendent Darren Fielke said in January.
“We continue to engage with them.
“They went through a pretty horrid Christmas without Gus, and we check-in with the family regularly.”
Police have previously stressed that no part of the investigation had turned up any suggestion of foul play.
Lamont was last seen by his grandmother at the family’s Oak Park Station homestead.
About 30 minutes later, he had vanished and a full-scale search was launched.
The four-year-old with blond curly hair has been described as a shy but adventurous child.
His family have said in a statement they are “devastated” and “deeply distressed” by his disappearance.
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