However, the Home Office, which must decide his fate, has been handed a psychiatric report downplaying fears that the 46-year-old would commit suicide.
The same doctor interviewed Mr McKinnon, who suffers from Asperger’s, in 2009 and concluded he was a suicide risk.
The development could pave the way for Home Secretary Theresa May to authorise Mr McKinnon's extradition to the US to face trial for hacking into military computers a decade ago.
Professor Declan Murphy assessed Mr McKinnon in 2009 at the request of the Briton's legal team. At that time he concluded Mr McKinnon would require one-to-one observation to prevent him taking his own life.
However, despite having been refused access to Mr McKinnon since then, in his latest report – seen by Channel 4 News, Prof Murphy wrote: "We judge the risk of suicide to be moderate.
"The risk of actual self-harm could be ameliorated by regular contact with mental health professionals and with supportive counselling and listening services of the type that are available within UK prisons."
He added that Mr McKinnon "did not express significant hopelessness or helplessness" and his "suicide plans are not well formulated", the programme reported.
By contrast, Prof Murphy wrote in 2009: "If Mr McKinnon is deported to the United States of America he will require (in my opinion) continual observation on a one-to-one basis during that time period, and for the rest of his incarceration.
"If this does not happen he is likely to make a serious attempt at suicide."
He warned: "Mr McKinnon stated that he would kill himself ... He now has a fixed idea, which is currently unshakeable, that his best outcome is to take his own life if deported."
Prof Murphy told the programme he could not comment on the change in his assessment while the case was still being considered by the Home Secretary.
But Mr McKinnon's mother Janis Sharp told Channel 4 News: "What basis could he possibly have to go against the expert opinions of four of the top people in the country, who say that Gary will absolutely take his own life?
"It's an in absentia report and it contradicts his previous face-to-face report. What did he base this on? It's a mystery to everyone."
Mr McKinnon, from Wood Green, north London, has been fighting the prospect of extradition to the US, where he faces up to 60 years in jail if convicted of hacking charges, since he was first arrested in 2002.
He admits hacking but claims he was looking for evidence of UFOs.
A Home Office spokesman said: "After consulting the chief medical officer, the Home Secretary instructed two independent experts to review the case and their report was sent to Mr McKinnon's representatives on February 24 in line with the directions of the court.
"Mr McKinnon and his legal team have until April 6 to respond and make any further representations.
"The Home Secretary will consider the report alongside all other relevant material and aims to reach a decision as soon as is consistent with dealing fairly and properly with this case."
In January, the High Court expressed concern over how long the case was taking to return to court, with two judges listing it for July in a bid to speed matters up.
They acted after hearing that Mrs May was "considering afresh" whether Asperger's sufferer Mr McKinnon should be extradited.
Arrested in 2002, and then again in 2005, an order for his extradition was made in July 2006 under the controversial 2003 Extradition Act between the UK and the US.
Critics claim it is one-sided and favours the US, but an independent review by former Court of Appeal judge Sir Scott Baker last year found it was both balanced and fair.
Shami Chakrabarti, director of civil rights group Liberty, said: "Three leading experts have described Gary McKinnon as a serious suicide risk.
"It's going to take more than one doctor miraculously changing his mind without even re-examining his patient to persuade anyone that an autistic man is fit for extradition."
"The risk of actual self-harm could be ameliorated by regular contact with mental health professionals and with supportive counselling and listening services of the type that are available within UK prisons."
He added that Mr McKinnon "did not express significant hopelessness or helplessness" and his "suicide plans are not well formulated", the programme reported.
By contrast, Prof Murphy wrote in 2009: "If Mr McKinnon is deported to the United States of America he will require (in my opinion) continual observation on a one-to-one basis during that time period, and for the rest of his incarceration.
"If this does not happen he is likely to make a serious attempt at suicide."
He warned: "Mr McKinnon stated that he would kill himself ... He now has a fixed idea, which is currently unshakeable, that his best outcome is to take his own life if deported."
Prof Murphy told the programme he could not comment on the change in his assessment while the case was still being considered by the Home Secretary.
But Mr McKinnon's mother Janis Sharp told Channel 4 News: "What basis could he possibly have to go against the expert opinions of four of the top people in the country, who say that Gary will absolutely take his own life?
"It's an in absentia report and it contradicts his previous face-to-face report. What did he base this on? It's a mystery to everyone."
Mr McKinnon, from Wood Green, north London, has been fighting the prospect of extradition to the US, where he faces up to 60 years in jail if convicted of hacking charges, since he was first arrested in 2002.
He admits hacking but claims he was looking for evidence of UFOs.
A Home Office spokesman said: "After consulting the chief medical officer, the Home Secretary instructed two independent experts to review the case and their report was sent to Mr McKinnon's representatives on February 24 in line with the directions of the court.
"Mr McKinnon and his legal team have until April 6 to respond and make any further representations.
"The Home Secretary will consider the report alongside all other relevant material and aims to reach a decision as soon as is consistent with dealing fairly and properly with this case."
In January, the High Court expressed concern over how long the case was taking to return to court, with two judges listing it for July in a bid to speed matters up.
They acted after hearing that Mrs May was "considering afresh" whether Asperger's sufferer Mr McKinnon should be extradited.
Arrested in 2002, and then again in 2005, an order for his extradition was made in July 2006 under the controversial 2003 Extradition Act between the UK and the US.
Critics claim it is one-sided and favours the US, but an independent review by former Court of Appeal judge Sir Scott Baker last year found it was both balanced and fair.
Shami Chakrabarti, director of civil rights group Liberty, said: "Three leading experts have described Gary McKinnon as a serious suicide risk.
"It's going to take more than one doctor miraculously changing his mind without even re-examining his patient to persuade anyone that an autistic man is fit for extradition."
