The PNG government plans to deport about 160 of the men whose applications for refugee status were rejected.
The government says asylum seekers who don’t leave voluntarily will be forcibly deported.
The PNG Supreme Court has ordered the closure of the centre where about 900 men have been detained four years to deter others from illegally entering Australia.
Journalist and detainee, Behrouz Boochani, said immigration officials offered a group of asylum seekers from Nepal between $10,000 and 15,000 dollars each to leave PNG. He said the men were also offered between $20,000 and $25,000 each, if they left as a group.
He said the men were told the financial incentives would reduce the longer it takes them to agree to depart.
The lawyer representing men in the detention centre, Ben Lomai, said the process for determining refugee status was flawed.
Lomai said he was applying for a court injunction to stop the deportations.