But even they say it is unlikely that China will let Liu go, which would seem like backtracking.
Liu, China's most prominent political prisoner, was diagnosed in May after his cancer had entered the final stages and was transferred to the hospital in the northeastern city of Shenyang.
In 2009, Liu was sentenced to 11 years in prison for inciting subversion, after he helped pen a political manifesto urging the Communist regime to initiate democratic 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.
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The official name of Xi's presidency is the People's Republic of China , something which the White House failed to take note. The gaffe has gone largely unreported in China because the local media have no motivation to mock Trump, Shi said.
The hospital in the north of the country where Liu, 61, was admitted said in a statement that he had been suffering from a stomach infection, peritonitis, organ dysfunction and septic shock, a critical condition that can lead to death, Efe news reported.
"We remain concerned that both Mr. Liu and his family are unable to communicate with the outside world and that he is not free to seek the medical treatment of his choosing", White House spokeswoman Sarah Huckabee Sanders said, reading from a prepared statement on the Nobel laureate during a briefing on Wednesday.
A spokesman for China's Ministry of Foreign Affairs, Mr Geng Shuang, on Monday (July 10) denounced calls for Mr Liu to be freed to go overseas as "meddling" by foreigners, even though the two foreign doctors, who were invited by the government to examine Mr Liu said that he could travel and that their hospitals would treat him.
Human Rights Watch's China director Sophie Richardson called the leak "grotesque propaganda".
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"It's also legitimate to question if the authorities are releasing the information about his worsening health as an attempt to delay and justify not allowing Liu Xiaobo to leave the country", Poon added. He was awarded the 2010 Nobel Peace Prize in absentia for his work campaigning for human rights in China. China has accused other countries of politicizing the writer's case and interfering in China's internal affairs.
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.
But a video of their visit released earlier this week showed the visiting doctors praising their Chinese counterparts.
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.
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The German embassy in Beijing later said in a statement the recordings were made against the expressed wishes of the German side.