Exiled Chinese dissident Yu Jie, a close friend of the couple, said he was "very sad and angry" at the deterioration in Liu's condition.
Liu was granted medical parole last month after being diagnosed with advanced liver cancer at the end of May.
Liu, 61, was jailed for 11 years in 2009 for "inciting subversion of state power" after he helped write a petition known as "Charter 08" calling for sweeping political reforms.
If he dies, Liu would become the first Nobel Peace Prize laureate to die in custody since German pacifist Carl von Ossietzky, who died in a hospital while held by the Nazis in 1938.
Geng reiterated that he hoped "relevant countries can respect the judicial sovereignty of China and not interfere in China's internal affairs under the pretext of an individual case".More news: Mithali Raj becomes highest run scorer in ODI
Liu's family has been notified of his condition and has refused intubation for him, according to a statement from the First Hospital of China Medical University in Shenyang.
Human rights groups said it was almost impossible to obtain independent information about Mr. Liu's health given that he is in a heavily guarded hospital and his wife, who is with him and also not free.
The Chinese hospital treating cancer-stricken Nobel laureate Liu Xiaobo offered a grim update on his health Wednesday, but human rights groups cautioned that the authorities may be manipulating the medical reports. On Monday, dozens of people waved banners and chanted slogans as they staged a sit-in protest outside the Chinese government's representative office, urging Beijing to allow Liu to be treated overseas.
Other prominent pro-democracy campaigners who left China on medical grounds, including Tiananmen student leader Wang Dan and veteran activist Wei Jingsheng, did so when China was still seeking membership in the World Trade Organization and made human rights concessions.
Beijing has rebuffed those calls, saying Liu is too sick to travel and is already receiving the best care possible.More news: OPEC figures show June oil output rise led by exempt nations
As China's government faces mounting global pressure to grant Liu his wish to leave the country for treatment, information control is a familiar strategy.
The United States repeated calls on Tuesday for Liu to be released and said it was ready to welcome him if he chose to be treated there.
Human rights groups questioned the motives behind the leak of a video showing the USA and German specialists by the bedside of a gaunt-looking Liu as they speak to his wife, Liu Xia, and the Chinese doctors.
The German statement also said the country's security services were steering Liu's treatment rather than the doctors.More news: Johanna Konta beats Caroline Garcia to reach Wimbledon quarterfinals