Yesterday, Shell announced it would offload 10% of its 34% stake in Woodside at a price of $42.23 a share, a move that is part of Shell's plan to boost its direct interests in assets.
The sale of 78.34 million shares has ended speculation that the Anglo-Dutch oil giant had been looking to launch another takeover bid for Woodside, but has left the company open as a potential takeover target.
The West Australian quoted Barnett as saying it was in Australia's and WA's interests for Woodside to remain an independent Australian company and he would do all in his power to block any foreign takeover.
"I would still have the view that it's important and in our national interest - certainly in our state's interest - for Woodside to remain an independent Australian company," he said.
"It is important for the international oil and gas companies to recognise that this is the only country in the world, outside of the United States, where they can develop these projects as purely private sector projects.
"We don't have requirements for production sharing, we don't have state [owned] oil and gas companies taking a part share of the project.
"That's a very privileged position and part of that is a mutual obligation to allow Australian companies to continue to operate, and Australian shareholders and superannuants to be involved in these developments.
"So it is very much in the broad interest of major [international] companies not to have a crack at Woodside, to let Woodside continue to grow as a mid-sized oil and gas company, but a very important Australian and WA company."
Barnett added he would not oppose other suitors, including BHP Billiton, taking a sizeable stake in Woodside as long as the company remained independent.
Some analysts had suggested Woodside could emerge as the next best option for BHP after its Pilbara iron ore merger with Rio Tinto collapsed and its Potash Corp bid was blocked by the Canadian government.
BHP Billiton Petroleum chief executive Michael Yeager had previously said the petroleum division was investigating oil and gas acquisitions for further growth; however, some analysts believe the company could look for other established oil and gas projects in North America.
Speaking at a lunch in Perth yesterday, Woodside chairman Michael Chaney said the company hasn't become a takeover target following Shell's sell-off, but added it would be natural for BHP and others to take a close look at Shell's remaining 24% stake.
"A whole lot of companies around the world will be dusting off the files and thinking about it," Bloomberg quoted Chaney as saying.
"We don't see this as a destabilising situation at all in the sense of making a takeover more likely.
"It would be surprising if in companies like BHP, people weren't running the ruler over it and thinking about it," he said.
Shares in Woodside dropped 6.3% to settle at $42.99 yesterday.