The speculation follows a deal that sees Sir Anthony increase his stake in Australia's fifth-largest media firm, APN News & Media, by selling it his stake in New Zealand media firm, Wilson & Horton Holdings, for £282.2m.
Wilson & Horton is New Zealand's largest publisher with titles such as the New Zealand Herald. The deal will also increase APN's share in the number one radio operator, New Zealand Radio Network, from 33.3% to 66.6%.
The deal will bolster IN&M's holdings in APN from 40% to 45%. IN&M, run by Sir Anthony O'Reilly, will now look at buying Fairfax, publisher of the Sydney Morning Herald, the Australian Financial Review and The Age. Sir Anthony failed to acquire the group in 1990.
Vincent Crowley, chief executive of APN, told the Sydney Morning Herald that "Fairfax has always been of interest to us", but that any move to buy Fairfax would hinge on Australian media ownership laws. These laws are set to be reviewed, possibly leading to a relaxation in cross-media ownership rules.
The sale of Wilson & Horton to APN is subject to approval by APN's shareholders.