"China is currently our second largest market. I believe it will become our first. I believe strongly that it will," the Xinhua News Agency quoted Cook as saying in an interview.
The report gave no details of when Cook thought China might pass the United States. Apple Inc. spokespeople in China did not immediately respond to a request for comment.
Apple has said sales in China more than doubled in 2010 and 2011 though growth has slowed in the past year.
Apple's iPhones, iPads and other gadgets are popular with China's highest-earning consumers but its fast-growing smartphone market is dominated by handsets that use rival Google Inc.'s Android system.
Cook was in Beijing to meet with Chinese regulators and managers of state-owned China Unicom Ltd., the first Chinese carrier to support Apple's iPhone.
Xinhua said Cook did not respond to rumors Apple might be developing a lower-cost iPhone for developing markets such as China.
Also in Beijing, Cook met the chairman of China Mobile Ltd., the world's biggest phone carrier, with more than 700 million subscribers. China Mobile has no agreement to support the iPhone, and adding it as a partner would help Apple increase its appeal in China.
China Mobile chairman Xi Guohua and Cook discussed "bilateral cooperation," the phone company said in a statement. It said release of other details was barred by a confidentiality agreement between the companies.
China Mobile says its network already is used by several million customers who brought in unlocked iPhones from abroad.
Apple opened a multistory flagship store on a prominent corner in Beijing's busy Wangfujing shopping district in October, raising its number of mainland retail outlets to 11. Independent stores also resell Apple products.
According to Xinhua, Cook responded to complaints about wages and other work issues at Foxconn, the Taiwanese company that assembles Apple's products in vast factories in China, by saying his company enforces strict codes of conduct for its suppliers.
"We care very deeply about every worker that touches an Apple product, whether they are making it, selling it, serving it or marketing it. We hold ourselves to a very high standard there," he was quoted as saying.
MORE HBJ HEADLINES
Before the robots rise up, they’ll make pizza U.S. rig count down 3 this week to 421 GM plans $290 million investment in Corvette plant United, flight attendants near tentative deal on new contract Atlas rocket launches for 1st time since March grounding Bellingham launches inspections of rental properties