Prime Minister Tony Abbott will use a meeting with US President Barack Obama at the White House on Thursday (US time) to seek the reopening of the agreement, News Corp Australia reports.
"While we are pleased with the US free trade agreement, that is not to say we could not get better access to US markets for some of our Australian agricultural products," Mr Abbott said.
Mr Obama will also receive the gift of a hand-made surfboard bearing the presidential seal.
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Mr Abbott praised the president as an "extremely charismatic and likeable individual".
"He is a man of extraordinary personal gifts. I certainly expect to like him at least as much this time as last time, considering the different position that I am in now."
The PM said he regretted his "lapse" last year in which he described Mr Obama as leading the most left-wing US administration in 50 years.
"One of the things I have learnt is not to be a commentator," he said.
Mr Abbott told reporters in New York he would be indicating to Mr Obama that "Australia is a very reliable friend".
"I doubt that America would have a more reliable friend anywhere in the world in what have been difficult and troubled times," he said.
