Australia's Prime Minister Anthony Albanese will meet Li, who is making the first visit to Australia in seven years by a Chinese premier, in Canberra on Monday.
Albanese said last week he would raise Yang's case with China's second-highest ranked official.
Yang, a pro-democracy blogger and spy novelist, is an Australian citizen born in China who was working in New York before his arrest at Guangzhou airport in 2019.
A Beijing court handed Yang a suspended death sentence on espionage charges in February, which the Australian government described as "harrowing".
The case has cast a shadow over a recent rebound in bilateral ties that followed several years of strained relations between China and Australia.
Yang has denied the charges.
In a statement on Sunday evening, Yang's supporters said Beijing's High People's Court had reviewed and upheld the lower court's sentence.
Australian diplomats were informed on May 30 and were denied a consular visit last week, and Yang was being moved to a permanent prison after five years in a state security detention centre.
"Our most immediate concern is that Yang's medical conditions remain serious and unaddressed," the statement said.
"For these reasons, we urge Prime Minister Albanese to use his meeting with Premier Li Qiang to directly demand that Yang be released on medical parole or otherwise be transferred to safety in Australia".
Yang's two sons, who live in Australia, have previously asked Albanese to seek their father's release on medical grounds.
Yang was told last year he had a 10cm cyst on his kidney that may require surgery, and has been unable to walk at times.
Foreign Minister Penny Wong told ABC television on Sunday that Australia "will continue to advocate for Dr Yang wherever we are able, and we will continue to advocate, including for appropriate medical treatment".
A suspended death sentence in China gives the accused a two-year reprieve from being executed, after which it is automatically converted to life imprisonment, or more rarely, fixed-term imprisonment.
The individual remains in prison throughout.
China's foreign ministry has previously said all procedures were followed in Yang's case.
