Reports suggest the pontiff wants to reach a deal next month, before the close of the Holy Year of Mercy on 20th November.
For decades the Communist Party in China has disputed bishops appointed by the Vatican, instead approving its own bishops who do not have official Church approval.
Catholic bishops, known as 'underground' leaders, face arrest and imprisonment in the country.
Some have criticised the Vatican's desire to ordain its own bishops in China, saying the religious institution is overlooking human rights abuses in the country.
Over the past year Chinese authorities have cracked down on Christian activities including worship and have undertaken a tough policy on cross removal from public buildings, for what it calls health and safety reasons.
The Guardian has reported that Belgian priest Jeroom Heyndrickx has been leading the negotiations.
He said: "There have been some efforts at dialogue in the past, but never so intensive and ongoing and with perseverance on both sides.
"The situation is more hopeful now than it has been in 65 years."
