Chinese President Xi Jinping refused to meet with the Pope in the context of the religious persecution of Christians.
Pope Francis has said little about China's human rights violations since the Vatican first entered into a provisional agreement with China in 2018.
That deal was meant to unify the country's 12 million Catholics, divided between the underground Church and the Communist-administered Chinese Patriotic Catholic Association, and clear a path for the appointment of bishops for Chinese dioceses.
Despite the deal, persecution of the underground Church has continued and, according to some, intensified. That deal is expected to be renewed for another two years at the end of the month.
According to the media, the source said the Vatican made "an expression of availability," and the Chinese side said they "appreciated the gesture" but that there was no free time in Xi's schedule.
Pope Francis was present at the religious conference in Nur-Sultan, the Kazakh capital, from September 13 to 15, called Astana.
At the same time, Xi was also in the capital city to meet Kazakh President Kassym Jomart Tokayev.
There are reports that Xi turned down a chance to meet the Pope and returned.
The meeting between the two would have been crucial in the context of the government's repression of Christians in China.
The Pope also revealed his willingness to visit China during his trip to Kazakhstan. Even then, Xi's refusal to visit the Pope drew criticism among European countries, including the Vatican.
Meanwhile, Xi held a meeting with Russian President Vladimir Putin in Kazakhstan.
The Pope and Xi arrived in Kazakhstan at the same time as the Vatican and China decided to renew a temporary agreement on the appointment of bishops in China and a cardinal preparing to stand trial in Hong Kong.
Xi has come under heavy criticism for overseeing the persecution of various religions in China, including Christians in the Xinjiang region.