Douglas Wood, a 63-year-old Australian engineer who lives in California, was abducted early this month by a group calling itself the Shura Council of the Mujahedeen of Iraq.
Australia's mufti, Sheik Taj El Din al-Hilaly, flew to Iraq to negotiate his release and last week reported having a telephone conversation with an Australian he believed to be Wood who said he was well.
The cleric, an Egyptian-born Sunni, has offered to swap places with Wood, who suffers from a serious heart condition, in a statement expected to be broadcast soon on Middle Eastern television, spokesman Keysar Trad said on Thursday in Canberra.
A spokesman for Wood's family told Reuters they were aware of al-Hilali's offer and appreciative of his efforts to free Wood.
But Australia's government reacted coolly on Thursday to the offer.
"But we don't want to see Australians held hostage full stop and we would like to see the unconditional release of Douglas Wood"
Australian foreign minister
The government, which has refused to negotiate with the hostage-takers, responded to Hilali's initiative by saying its position was that Wood should be released unconditionally.
"In a broad sense we appreciate that Sheikh Al Hilali is making an effort to assist with the release of Douglas Wood and we appreciate all efforts that are being made," Foreign Minister Alexander Downer said.
"But we don't want to see Australians held hostage, full stop, and we would like to see the unconditional release of Douglas Wood," he said.
"For the mufti of Australia to make that offer - it's certainly a very attractive offer to any group, to hold a very prominent person and let their captive free so he can seek medical treatment," Trad told Nine Network television.
Al-Hilali has visited Iraq in a bid
to have Douglas Wood released
"They promised to set him free before without these conditions but the mufti is now trying to force their hand and trying to get them to make a move and release Mr Wood," he said.
Wood's captors have released two DVDs showing their hostage with rifles pointed at his head as he begs the Australian government to pull its troops out of Iraq.
The government refuses to bend to their demands.
The cleric also asked his captors to show proof that Wood is still alive by producing a new videotape.
"I announce my sincere readiness to hand myself over to the captors to be a hostage in exchange for the sick Australian citizen, till the conditions of the brotherly captors are met in the way they want," al-Hilaly said in his statement.
Ikebal Patel, treasurer of the Muslim group Australian Federation of Islamic Councils, said al-Hilaly was negotiating with Aljazeera to broadcast his offer.
The cleric was not concerned for his safety in becoming a hostage, Patel said.
"He is very respected in the Middle East and around Iraq as well," Patel told Seven. "He has done a lot of good work in the last two weeks in Iraq and we feel that that will carry him through."
Wood needs daily medication for his heart disease, high blood pressure, high cholesterol and rheumatoid arthritis.
Australia sent 2000 troops to back US and British forces in the Iraq invasion and almost 1400 Australian troops remain in the Middle East.