Jim Macken, who is 88, said he had written to Immigration Minister Peter Dutton to offer a “body swap”.
“I understand this is an unusual request but I offer it in complete sincerity,” Mr Macken wrote.
Australia processes migrants and refugees on the Pacific island of Nauru and on Manus island, Papua New Guinea.
The government has faced heavy criticism over conditions at the detention centres, both of which are run by private companies.
In the letter, seen by Australian media, Mr Macken said: “My reason for making this proposal is simple. I can no longer remain silent as innocent men, women and children are being held in appalling circumstances on Manus Island and Nauru.
“It is even worse that they are being held in these dangerous and inhospitable conditions in order to ensure no other asylum seekers and refugees attempt to come to Australia for protection.
“The Australian government is essentially treating refugees in these camps as human shields and this is utterly immoral. As this is being done in my name I cannot remain silent.
“I offer this proposal as a way forward for at least one refugee. This would allow one person currently held on Manus Island or Nauru the right to be an Australian citizen. I would consider it a privilege to live out my final years in either Nauru or Manus Island in his or her stead.”
Mr. Macken reportedly offered to relinquish his Australian citizenship if necessary.
A spokeswoman for Mr. Dutton said the minister’s office was checking to see if it had received the letter, which was sent a month ago, and declined to comment further.
Mr. Macken also wrote to Prime Minister Malcolm Turnbull and Labor party leader Bill Shorten, urging them to “err on the side of compassion and justice” and end offshore processing.
A spokesman for the prime minister declined to comment.
Speaking to the Guardian, Mr Macken said he had “nothing to lose” by making his offer. -BBC