Woodside shares ended down 2 cents in a broader market that rose 0.8% and while BHP rose 1.3%.
The report in The Australian's Data Room column followed a Bloomberg report which said that mining group BHP was considering selling its oil and gas business, which includes assets off Australia and Trinidad and Tobago and in the Gulf of Mexico.
BHP and Woodside declined to comment on what both companies called "market speculation".
"We remain focused on the continued safe execution of our Sangomar project in Senegal and achieving our targeted final investment decision on the Scarborough and Pluto Train 2 developments in Western Australia," a Woodside spokesperson said in an emailed comment.
The fall in Woodside's shares highlighted investors' fears that Woodside would need to sell new shares to buy some or all of BHP's oil and gas assets, valued at around $10 billion to $15 billion, which would come on top of spending on its Australian and Senegal projects, analysts and an investor said.
"That's unpalatable," said Simon Mawhinney, Chief Investment Officer at Allan Gray Australia, a Woodside shareholder.
He said it would be disappointing if Woodside were to buy any or all of BHP's petroleum assets "unless BHP were to gift them."Credit Suisse analyst Saul Kavonic said there would only be a limited pool of buyers for BHP's Australian assets, partly because they include ageing assets which face hefty decommissioning costs within the next 10 years.
He also said Woodside would be a "lead candidate" to buy BHP's Australian petroleum assets as Woodside already has stakes in two of them - the North West Shelf LNG project and the Scarborough gas field.
BHP Chief Executive Mike Henry said as recently as March that BHP sees "attractive value and returns to be generated for shareholders for the next decade" from oil and gas, but would sell off more mature assets.
(Reporting by Sonali Paul. Editing by Jane Merriman)
By Sonali Paul