The items, which are being reported as bones, were found last Wednesday and are currently undergoing testing to confirm their identity.
Matthew Leveson was last seen outside the ARQ nightclub in Darlinghurst with his boyfriend, Michael Atkins, on September 23, 2007.
Atkins was initially charged with his murder, but later acquitted in 2009.
After admitting to lying at an inquest into the suspected murder, Atkins was at risk of being charged with perjury and contempt of court. He was granted immunity of prosecution, however, when he helped police zero in on the potential burial site of Mr Leveson.
Two earlier searches of the area had revealed nothing.
The inquest into the death of Matthew Leveson is scheduled to resume in August.