Chancellor Angela Merkel's spokesman Steffen Seibert voiced "the very greatest concern" over reports that Liu's health had further deteriorated, calling the family's situation "dramatic".
The democracy advocate's hospital said Wednesday that 61 -year-old Liu had suffered respiratory failure after it earlier reported he had organ failure.
"Germany stands ready to host and medically treat" the Chinese activist, who was sentenced to 11 years in prison in 2009 for "subversion" after calling for democratic reforms, Seibert said.
"The German government appeals to the Chinese leadership to prioritise the humanitarian aspects of this case and allow Mr Liu and his family to immediately leave the country."
Liu was released on medical parole after being diagnosed with terminal liver cancer last month.
One of his family friends told AFP that he had sent a letter from Liu's wife to the US and German governments expressing the couple's wish to leave China.
The Chinese government has rebuffed international appeals to let Liu seek treatment abroad, saying he is getting the best possible care from top domestic doctors.
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 while held by the Nazis in 1938.
Seibert said the latest reports on the dissident's state of health "raise the question of whether Mr Liu's cancer should have been diagnosed and treated far earlier".
Liu was arrested in 2008 after co-writing Charter 08, a bold petition that called for the protection of basic human rights and reform of China's one-party Communist system.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)