The manuscript, which is thought to date from between 15, appears to show a small kangaroo within the letters of its text.
If the image actually is a kangaroo, the drawing suggests that Portuguese explorers may have discovered Australia before the first recorded European landing on the continent by Dutch navigator Willem Janszoon in 1606.
Over recent decades Australia has sought to strengthen its relationship with Asian countries, with this becoming the focus of the country's network of diplomatic missions.
Australia was one of the founders of both the United Nations and the South Pacific Commission (1947), and in 1950, it proposed the Colombo Plan to assist developing countries in Asia.
The document, which contains text or music for a liturgical procession, was recently acquired by the Les Enluminures Galley in New York, which has valued the item at ,000 (£9,174).
It was previously in the possession of a rare book dealer in Portugal.
Other researchers speculate that the manuscript may have come from slightly after Janszoon's arrival in Australia, or may date from a 1526 Portuguese voyage to Papua.
The gallery plans to display the document as part of an exhibition.