Fresh from an attention-grabbing tour of the United States and Cuba, Pope Francis has his sights on another destination. "I'd really love to go to China," the Catholic leader told reporters on a flight back to Rome on Monday, the Italian news agency ANSA reports. "I love the Chinese people."

It's an ambitious target. If Francis were to visit mainland China, he would be the first pope to do so. The Vatican and Beijing haven't had diplomatic relations since 1951, and they remain divided over a variety of issues. "I hope there is a possibility to have good relations with China," the pope told reporters. "We have contacts, we talk. It's necessary to keep going."

Speculation about a potential papal visit to China has been mounting for years. In March 2014, Francis hinted at warmer relations with Beijing in an interview with an Italian newspaper. "I sent a letter to President Xi Jinping when he was elected, three days after me," the pontiff told Corriere della Sera. "And he replied to me." Later, while flying over China after a trip to South Korea in August 2014, Francis sent a telegram addressed to Xi and the Chinese people. “I extend my best wishes to your excellency and your fellow citizens, and I invoke divine blessings of peace and well-being upon the nation,” the telegram read.

The pontiff's predecessor, Benedict XVI, also had expressed a desire to visit China, but under Francis these hopes seem have grown more concrete. The Catholic leader appointed Pietro Parolin, a cardinal with experience working behind the scenes with China, as his secretary of state. Furthermore, Francis has gained a reputation as someone willing to take risks, and, as a Jesuit, he is a member of a congregation with significant historical links to China.

Reaching an agreement for a visit will not be easy. Since the Communist Party took power in 1949, both the Vatican and Beijing have been locked in a battle for control of China's Catholic population. Catholic missionaries had been operating in China since the 13th century, at points causing conflict: In 1715, a papal decree that condemned traditional Chinese rites and Confucian rituals sparked a backlash in the country. After the Chinese Communist Party came to power, the Catholic Church was officially viewed as a form of Western imperialism. Catholics, along with other Christians, were treated with suspicion.

In 1957, Beijing set up the Chinese Patriotic Catholic Association (CPCA) to exercise control over China's Catholics. This association rejects the authority of the Vatican and appoints its own bishops. According to the Pew Research Center's 2011 estimates, about 5.7 million of China's 9 million Catholics are associated with the CPCA and its churches. The rest worship with unregistered congregations that remain loyal to the mainstream Catholic faith. These Christians face persecution from the state, with their places of worship at risk of demolition.

This split has been a major source of strife between the two sides. The Vatican has excommunicated a number of Catholic bishops appointed by Beijing, with Benedict complaining that the persons nominated were "sometimes not even baptized." Chinese authorities have hit back at the excommunications, with a spokesman for the State Bureau of Religious Affairs saying that the act was "extremely unreasonable and rude" and that it "severely hurt the feelings of Chinese Catholics and made its members feel sad."

Another point of contention is the Vatican's continuing diplomatic relations with Taiwan. China has said that the Catholic Church must sever its ties with the Taipei government, which Beijing considers a renegade province, before the two powers can reestablish formal diplomatic relations. So far, the Vatican has not agreed to this demand.

It is possible, however, that Francis has compromised already. He did not meet with the Dalai Lama during the Tibetan leader's visit to Rome last year, a break with tradition that many interpreted as an attempt at appeasing Beijing. Some, such as Cardinal Joseph Zen Ze-kiun, a former Hong Kong bishop, have warned that a visit by Francis to China would play further into Beijing's hands. “I would tell him now: ‘Don’t come, you would be manipulated,’” Zen told Corriere della Sera last year.

Still, Francis's unprecedented celebrity may present a problem for China. On Weibo, a significant number of Chinese micro-bloggers have followed the pope's trip to the United States with interest. "The Catholic church is getting stronger," one user commented on a post featuring photographs of the huge crowds that greeted Francis in New York. And Xi can't be unaware of the popular momentum behind the pope — he delayed his visit to Washington last week so as not to compete for attention with the Catholic leader.

Xu Yangjingjing contributed to this report.

More on WorldViews