Nils Melzer, UN's special rapporteur on torture, is expected to make his appeal to the UK government on Friday, the Guardian reported.
It comes after Assange was said by his lawyers to be too ill to appear by video link for the latest court hearing of the case on Thursday.
Assange has been moved to the health ward of Belmarsh prison, London, where he has been serving a 50-week sentence for skipping bail while fighting extradition to the US.
He is accused of violating the Espionage Act by publishing secret documents containing the names of confidential US military and diplomatic sources.
After meeting Assange earlier this month in the company of medical experts who examined him, Melzer fears the Australian's human rights could be seriously violated if he is extradited to the US and condemns what he describes as the "deliberate and concerted abuse inflicted for years" on him.
Assange was arrested in April after Ecuador revoked his political asylum and invited police inside the country's Knightsbridge diplomatic premises, where he had sought refuge in 2012 to avoid extradition to Sweden over allegations of sexual assault, which he has denied.
"Physically there were ailments but that side of things are being addressed by the prison health service and there was nothing urgent or dangerous in that way," Melzer said.
Assange could face decades in a US prison after being charged with violating the Espionage Act by publishing classified information through WikiLeaks.
Prosecutors earlier this month announced 17 additional charges against him for publishing hundreds of thousands of secret diplomatic cables and files on the wars in Afghanistan and Iraq.
The 47-year-old was previously charged with working to hack a Pentagon computer system, in a secret indictment that was unveiled soon after his arrest in April.
( With inputs from IANS )