Britain's Sunday Times reported that BHP was in talks to buy Royal Dutch Shell's 24 percent stake in Woodside, followed by a full takeover bid worth some US$50 billion.
An Australian spokeswoman for BHP said the company would not comment on the reports, but shares in Woodside rose to Aus$50.46 in early Monday trade, adding 6.77 percent, or Aus$3.20, to Friday's close.
The Australian Financial Review on Monday said BHP and Shell had been in detailed talks on a possible deal but indicated no decision was imminent.
It quoted Shell Australia country chairwoman Ann Pickard as telling reporters in Perth on Sunday there were "no commercial discussions" on the company's Woodside holding and she was "not in a hurry to do anything" with it.
Woodside refused to comment on the latest reports but in November the company admitted it could be of interest to BHP Billiton after Royal Dutch Shell sold a US$3.3 billion stake.
At the time, Woodside Chairman Michael Chaney said "it is possible" BHP would be interested, especially given it had "run the ruler" over Woodside in the past. "It is natural that they'd be doing so again," Chaney said.
Woodside is one of the world's leading producers of liquefied natural gas and is planning to expand and develop more LNG assets, including those off Western Australia.
Western Australian Premier Colin Barnett said he would discourage a takeover of Woodside, saying the company "seems to be under siege".
"I just urge you hands off Woodside," he told a conference on Monday.