The United States and Germany voiced concerns over the 61-year-old writer after the hospital treating him said yesterday he had organ failure and difficulty breathing.
The doctors said Liu needed to be on artificial ventilation to be kept alive, but his family declined, according to the First Hospital of China Medical University in the northeastern city of Shenyang.
Human rights groups have decried the lack of independent reports about Liu's health, accusing the authorities of manipulating information as the heavily-guarded hospital's website has been the only source of medical updates.
Liu, who was sentenced to 11 years in prison for "subversion" in 2009, was admitted to the hospital early last month after he was transferred from prison due to late-stage liver cancer.
His wife, the poet Liu Xia, has been by his side, but her ability to communicate with the outside world is restricted. Authorities have kept her under house arrest since 2010.
German government spokesman Steffen Seibert said Berlin "stands ready to host and medically" treat him.
The latest health updates "raise the question of whether Mr Liu's cancer should have been diagnosed and treated far earlier," Seibert said.
Taiwan's President Tsai Ing-wen also called on Beijing to free Liu and reiterated her offer to have Liu treated on the self-governed island, which China considers a breakaway province.
A German and a US doctor visited Liu last weekend and said he was still strong enough to fulfil his wish to travel overseas, but the hospital has issued increasingly pessimistic reports every day since then.
Liu risks becoming the first Nobel Peace Prize laureate to die in custody since German pacifist Carl von Ossietzky, who passed away in a hospital under the Nazis in 1938.
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