One of the three suspects is Suddaen's elder brother, Warut Satchakit.
Alan Hogg was shot while his wife Nhot Suddaen was bludgeoned to death with a hammer at their villa in the northern province of Phrae by men paid 50,000 baht (S$2,105).
Three suspects have been held. The Lao man said he bought the pickup from three men on September 21.
The men also reportedly implicated Hogg's brother-in-law, Warut Satchakit, in the crime. "They said that the victims were then buried in the garden".
Mr Warut reportedly told investigators that the dead couple had repeatedly criticised him and "he got exhausted of it" and planned their deaths.
Major General Praputsra said that Alan's brother-in-law denied any involvement in their disappearance and police did not have enough evidence to charge him.
Police and rescue workers had previously dug there after a small backhoe was found parked next to freshly turned soil but had found nothing.
"The three men conspired in the murder of the couple and our investigation is ongoing to determine exactly who did what", deputy police spokesman Colonel Kissana Phatanacharoen told Reuters. They had built a large and well-appointed house.
Edinburgh-born Hogg, a retired engineer, and his wife had been reported missing by friends last week, Sky News reports, after they failed to turn up to a pre-arranged meeting.
Officers continued their hunt today checking the couple's home, swimming pool, reviewing CCTV footage from the area and ordering police divers to scour nearby rivers.
He was charged with theft and released on bail - but has since fled.
Included in the latest interrogations was Khun Nod's brother, Warun Satchakit, who was first set free on bail after initial questioning over the couple's stolen white pick up, but was released before his later arrest when the auto was located last Sunday.