Referring to a recent report by Catholic News Agency: "Pope Francis pursues a thaw in relations with mainland China", it is my hope that some background information may be useful.
Before the communists came to power in China, the Vatican had diplomatic relations with Chiang Kai-shek's Government through its nuncio, Msgr Riberi.
Although Chiang, after being defeated, escaped to Taiwan in 1949, Msgr Riberi resisted leaving China.
Only because of his being expelled in 1951 by the Communists did he leave China, but continued to seek every opportunity to return to the mainland, until the Vatican transferred its nunciature (and Msgr Riberi) to Taiwan.
At that time, Chiang's Government was still recognised by the UN as China's legitimate government.
However, when on 25 October 1971 the UN withdrew its recognition of Taipei by recognising Beijing, the Holy See did not switch its diplomatic recognition from Taiwan to Beijing.
In the years that followed other countries including the US established diplomatic recognition of Beijing, thereby leaving the Vatican as the only important country that still recognises Taipei.
This is strange because, contrary to the Holy See's firm attitude in 1949 of trying to stay in China even under the new Communist regime, this time, by failing to recognise Beijing, it deprives itself from having any say in the running of the Catholic Church on the mainland, because of Beijing's motto of "no recognition, no dialogue"!
Worse, because of the absence of a dialogue, the Chinese Government started to select and appoint its own bishops as they are reluctant to accept bishops who have to obey a Pope who – as a Head of State (i.e., the Holy See) – does not recognise them but rather Taiwan's breakaway Government through the nunciature in Taipei.
Consequently, as long as the Holy See does not substitute Beijing for its diplomatic ties with Taiwan (by cutting its diplomatic ties with Taiwan), as most countries did in the 1970s, a real dialogue with Beijing seems unlikely.