The government has made a new offer to the Sri Lankans on board the Australian Customs vessel, who have been on the vessel for more than two weeks, although some media reports suggest the asylum seekers have already rejected the deal.

Under the offer, those already recognised as refugees by the United Nations High Commissioner for Refugees (UNHCR) have been promised resettlement in Australia within a month.

Those not yet classified as such by the UNHCR would be resettled within 12 weeks if their claims are proved.

But the catch is they must disembark and stay in an Indonesian detention centre while their claims are processed.

The ABC says 30 of the 78 asylum seekers are believed to have already been deemed refugees by the UN agency.

"We're hopeful that this will be finalised soon," Immigration Minister Chris Evans told ABC radio.

Asked if he had any reason to be hopeful, Senator Evans replied: "Hope springs eternal."

The current arrangements were the best way to get the result the government wanted, Senator Evans said, and that was to get them off the boat.

The asylum seekers were wanting the most comfortable form of accommodation and there may be different options for different persons, he said.

"But the detention centre is a modern one; it's probably the best one in Indonesia. We think it's appropriate for certain clients to be accommodated there. The Indonesians have made it available."

Senator Evans would not say how many of them Australia would accept under a resettlement program, but said the government was considering a "sizeable amount".

Despite the government's optimism, the Australian newspaper reported on Thursday that the asylum seekers have already rejected the latest offer.

A note by the asylum seekers said the government gave a "lie letter to cheat us".

"We don't buy it", a section of the note published in The Australian says.