Detainees fear they won't be safe at three other facilities they are meant to relocate to in and around the island's main town of Lorengau.
The group believes their constitutionally protected human rights are being breached by the removal of basic services, including water and electricity.
PNG lawyer Ben Lomai is expected to lodge a legal application on Tuesday morning, The Guardian reports.
He said many of the men were "involved" in drugs and some had threatened to rape local wives and children.
The ABC reports about 90 asylum seekers remained at the centre on Friday, with some reporting they had been given a deadline of Monday to leave.
Manus Island's police commander has ruled out the use of force to remove the men.
Extra PNG police have been deployed to the island after many locals threatened to use violence to stop the asylum seekers relocating.
Two of the three centres earmarked for the detainees are still not fenced or guarded.
MANUS Island detainees are expected to launch legal action over the closure of Australia's immigration detention centre.