SYDNEY (AFP) - Australia has offered to pay the cost of imprisonment for two drug smugglers on death row in Indonesia if they are spared the firing squad, in another bid to save their lives.

Foreign Minister Julie Bishop made the offer in a letter to her Indonesian counterpart Retno Marsudi as Canberra explores all avenues to convince Jakarta not to execute Andrew Chan and Myuran Sukumaran.

The pair are among several foreigners, including a Frenchman, a Brazilian, three Nigerians and convicts from the Philippines and Ghana, who could be shot dead any time for drug-related crimes.

Bishop suggested a prisoner-swap with Indonesia in a tense phone call with Marsudi on March 3, which was rejected, and in a follow-up letter, she said Canberra was willing to pay for the pair's life imprisonment costs.

"As discussed, the Australian government would be prepared to cover the costs of the ongoing life imprisonment of Mr Chan and Mr Sukumaran should a transfer not be possible," Bishop wrote in the letter, released by her department.

"The vast majority of Australians very strongly support the government's efforts to seek clemency for Mr Chan and Mr Sukumaran.

"We would not want to see their execution compromise the strong ties we have worked so hard to foster over many years," she added.

In a reply, also supplied by Bishop's office, Marsudi again rejected a prisoner swap but did not touch on the reimbursement offer.

Australia has repeatedly called for clemency, fraying ties between the neighbours.

On Wednesday, Australia's most senior Islamic cleric, the Grand Mufti Ibrahim Abu Mohamed, travelled to Jakarta to plead with authorities in the world's most populous Muslim-majority country to spare the men.

Sukumaran and Chan, ringleaders of the so-called "Bali Nine" drug trafficking gang, were sentenced to death in 2006 for trying to smuggle heroin out of Indonesia.

They recently lost their appeals for presidential clemency, typically the final chance to avoid the firing squad, and have been moved to Nusakambangan prison island off Java, where their executions are due to take place.

Their lawyers have mounted a final legal challenge to Indonesian President Joko Widodo's decision to reject their pleas for clemency, claiming he failed to assess their rehabilitation or give reasons for his decision.

The appeal was due to be heard on Thursday.