On Monday Sumarno Lamundi, a police inspector, said officials have not ruled out the possibility that Naan was killed because he spearheaded anti-logging efforts by his Penan tribal community.
"We are still investigating what happened, but there are no suspects so far," he said. "Everything is still under consideration. We have not rejected any possibility."
Lamundi however refused to say whether authorities have found any evidence of murder or how long the investigations are expected to take.
Naan was on the forefront of the Penan's fight against the state's timber trade, which tribals blame for destroying their ancestral lands and snatching away of customary rights over forests.
Sarawak state authorities and timber companies reject the charges.
Naan's death came ahead of what some villagers believe are plans by timber companies to resume logging, which has stalled in recent years in areas surrounding Long Kerong, the village that Naan led.
He was also was an initiator and key witness in an unresolved Penan land rights court case.
Local media have speculated that the Penan chief might have died in an accident, but anti-logging activists suspect that foul play was involved.
Last month Micheal Ipa, Naan's nephew, said some Penans "believe he has been killed by people involved in logging".
The Observatory for the Protection of Human Rights Defenders based in Geneva voiced "deep concern" about Naan's death, saying it "might be the result of his human rights activities in favour of indigenous issues".