(Reuters) - Qatar Airways is in talks to buy up to a 20% stake in Bain Capital-owned Virgin Australia, the Australian Financial Review (AFR) reported on Wednesday, as carriers fight for more market share in the country against dominant airline Qantas.

U.S. private equity firm Bain Capital had aimed for a A$1 billion ($665.5 million) listing of Virgin on the Australian Securities Exchange but the plan was delayed, Reuters reported last year.

Government-owned Qatar Airways could announce its plans regarding the stake buy as early as next week, the AFR reported.

Bain Capital and Qatar Airways declined to comment.

Qatar Airways has shared a tumultuous relationship with Australia in the recent past after its attempt to increase its air presence in Australia was blocked by the Labor government.

($1 = 1.5026 Australian dollars)