Indonesian President Susilo Bambang Yudhoyono received Australia's highest civilian honour at a ceremony in Canberra this week.
He was appointed an Honorary Companion in the General Division of the Order of Australia.
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Prime Minister Kevin Rudd indicated Mr Obama was not in line for similar recognition.
"Not so far as I'm aware," he told Fairfax Radio Network on Friday, adding it was his call.
"But we're very mindful of what President Yudhoyono has done over a period of eight or 10 years now.
"The Bali bombings went very much to the hearts and lives of many many Australians."
Mr Rudd said the Indonesian president was honoured for his work in tracking down terrorists after the Bali bombings, as well as for strengthening democracy.
