A senior US government official had said last week that Washington was keen to have India, Japan, and Australia on board for a "productive" engagement, while Japanese Prime Minister Shinzo Abe is likely to propose the same arrangement between the four powers when President Donald Trump visits Tokyo on Monday.
India has responded positively to the proposal, saying it has "an open mind to cooperate with countries with convergence but obviously on an agenda which is relevant to us".
The Chinese Foreign Ministry said it has noted the development and hopes that such an arrangement will promote mutual trust among countries in the region and not harm Beijing's interests.
"China has noticed the relevant news reports. We hope the collaboration among relevant countries could comply with the trend of times, which refers to peace, development, and cooperation and shared benefits, and also conform to the prospects of the regions and nations for common security and development," the ministry told IANS in a statement.
"We hope it would be beneficial for improving the mutual trust among countries and regions, at the same time safeguarding and promoting peace, tranquillity, and prosperity within the area, without targeting or damaging a third party's interest," it added.
The US, India, Japan and Australia have growing concerns over China's increasing assertiveness in the Indo-Pacific region and its ambitious Belt and Road connectivity project.
Last week, Alice Wells, Acting Assistant Secretary for South and Central Asian Affairs, said the US was "looking at a working-level quadrilateral meeting in the near term".
She also referred to the freedom of navigation without mentioning the disputed South China Sea, where the US and Chinese navies have had several run-ins.
During his India visit last month, US Secretary of State Rex Tillerson reportedly talked about building a network of roads and highways with India that will be an alternative to China's Belt and Road initiative.
India opposes the multi-billion dollar Belt and Road project whose key artery, the China-Pakistan Economic Corridor, cuts through the part of Kashmir held by Islamabad.
A section in the Australian government also believes that it is not a mere economic project, as claimed by Beijing, but also a geopolitical one.
After returning home, Mr Tillerson had described the US, Japan, India and Australia as "anchors" in the Indo-Pacific region which includes the Indian Ocean and the South China Sea.
China's presence has increased in the Indian Ocean, causing India worry.
Japan also worries about China's growing naval strength. Both powers have disputes over the islands in the East China Sea.