Beijing also plans to start talks on a free trade agreement this week as it seeks to secure sources of oil and broaden its trade relationships.
The deal is designed to reduce tariffs and simplify the flow of goods and investments.
The GCC groups are Kuwait, United Arab Emirates, Bahrain, Oman, Qatar and Saudi Arabia.
Energy demand in the world's most populous country has outpaced supply, creating power shortages in three-quarters of mainland China's 31 provinces and regions last year.
Planning for the future
China, the world's second largest oil consumer, is establishing strategic oil reserves and trying to diversify its supply - much of which already comes from the Middle East.
The free trade deal would be China's second with a regional group after a pact it has in the works with the Association of South East Asian Nations.
"We are prepared to provide China with its energy needs," it quoted Faisal al-Ghais, council representative and Kuwait's ambassador to China, as saying.
China and the Gulf Cooperation Council could strengthen cooperation in oil exploration and investment, he said.
"We are prepared to provide China with its energy needs"
Kuwait's ambassador to China
His comments come ahead of a visit this week to Beijing by a team of finance ministers and other officials from the GCC and by Secretary-General Abd al-Rahman al-Attiya.
Kuwaiti Prime Minister Shaikh Sabah al-Ahmad al-Sabah will also visit China this week.
The newspaper said China's trade with the Gulf Cooperation Council was $17bn last year, an increase of 46% from 2002.