American Airlines is looking to become the second big carrier in the United States to buy its way into capturing more of the big and growing business of flying to China.

China Southern, the biggest airline in China, the world's most populous country, said on Sunday that it was in talks with American about a "major strategic cooperation" that may involve a share sale or unspecified other business cooperation. If one materializes, a deal would tie American, one of the United States' big three carriers, together with one of China's big three state-run airlines.

Any agreement would be subject to board and regulatory approvals, China Southern said in a stock exchange filing in Hong Kong, near the carrier's base in the southern Chinese city of Guangzhou.

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It would be the second such agreement between major airlines in the two countries. Delta Air Lines reached a deal in 2015 to pay $450 million for a 3.55 percent stake in China Eastern Airlines, another Chinese carrier with headquarters in Shanghai.

American, based in Fort Worth, would probably gain only a small stake in China Southern if a deal happened, given the sheer size of the companies and reluctance in both countries to give foreign investors meaningful say in how an airline is run. But a deal could help American capture more traffic between the United States and China through arrangements like code sharing, an industry term for a partnership that allows two airlines to more easily book passengers on each other's flights.

"The share purchase is kind of cosmetic in a way, because the whole thing is about code sharing and putting passengers from China onto the U.S. aircraft," said Geoffrey Cheng, the head of transportation and industrial research at Bocom International in Hong Kong.

Today, Chinese airlines account for more than 60 percent of assigned flight routes between China and the United States, said Corrine Png, a longtime transport industry analyst in Singapore. Among American carriers, United is the most established thanks to a partnership with Air China, the third major Chinese airline, based in Beijing. It has a route share of about 20 percent, Ms. Png said, while Delta and American each have a share of about 8 percent.

Much of the growth is from the China side, where traffic from outbound visitors more than doubled between 2010 and 2015, according to official statistics. Chinese airlines are better positioned to tap that market because of to their home-carrier advantage and their deep networks, which reach into the Chinese hinterland from the aviation hubs of Beijing, Shanghai and Guangzhou.

"The point is there are more Chinese travelers heading to the U.S. than in the U.S. and heading to China," Mr. Cheng said.

China is already the fifth-biggest source market for tourism to the United States, and Chinese visitor arrivals are forecast to more than double by 2021, according to an estimate by the United States government. By then, China will become the third-biggest overall overseas market for the United States after Mexico and Canada.

In addition to their lack of networks in the Chinese interior, American carriers have also struggled to add new routes to China's main international hubs because of capacity constraints.

Government-to-government agreements on the number of cross-border routes are reciprocal. But in recent years, traffic at airports in cities like Beijing and Shanghai has been rising fast, and it may take years before new runways or terminals can come online to increase the number of available landing slots at favorable times.

As a result, foreign carriers "try to work around this, and one way is to invest in a Chinese carrier and hopefully gain market access that way," said Ms. Png, the transportation industry analyst.

For China Southern, tapping a bigger foreign market makes sense as a way to catch up with domestic rivals like Air China and China Eastern that draw a larger share of their own revenue from overseas routes.

Ms. Png said a tie-up with American Airlines could take advantage of China Southern's base in Guangzhou, which does not have the same capacity constraints as Beijing.