Etihad, which has been looking at a possible investment in loss-making Italian airline Alitalia, declined to comment on the report.
Etihad is already a major shareholder in Virgin Australia Holdings, which has been engaged in a brutal price and capacity war with flag carrier Qantas Airways.
Qantas has long complained that Etihad and by extension Virgin, have benefited from subsidies from the Gulf state, something Etihad management has repeatedly denied.
Qantas has been lobbying for government support and changes to the law that limits its foreign ownership.
The newspaper said industry sources had provided the document, which had circulated among the management ranks of Etihad's competitors, such as Qantas and Emirates.
The Australian and International Pilots Association said the claims of support from the royal family needed to be checked and action taken to level the playing field.
"Etihad's contribution to Virgin's A$350 million ($322.60 million) equity issue last year was critical to the issue's success. We now know this contribution was backed by the interest-free generosity of the Abu Dhabi royal family," said AIPA President Nathan Safe.
"Such an obviously unfair distortion of competition would never be allowed in any other sector of the Australian economy and it should not be allowed to continue in aviation."
Virgin Australia did not immediately respond to requests for comment.
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