In a statement made over the weekend, the Home Office said it had agreed to delay extradition proceedings against McKinnon, pending a fresh consideration of the evidence, focussing on his medical condition.
McKinnon's lawyer, Karen Todner, told reporters that she and her client take some hope from this.
Todner has been quoted by the BBC as saying she hoped Home Secretary Alan Johnson would "show some compassion to someone who is extremely vulnerable".
"It does not matter if it takes some time to consider it, as long as they give it proper consideration", she said.
"We appreciate the Home Secretary may feel otherwise, but very eminent lawyers have given the advice that he does have the power to intervene, in fact we would say he has a duty to intervene.
"We hope he will stop this extradition process, and of course there is still the option to prosecute him (McKinnon) here."
As previously reported by Infosecurity, McKinnon - who was arrested in 2002 after allegedly hacking into computers belonging to the US Army, US Navy, US Air Force, Department of Defense and NASA - has been diagnosed with Aspergers syndrome, a mild form of autism, and concerns have been raised as to his well-being if he were to be extradited.
Unconfirmed sources now suggest it is likely that McKinnon may be tried for his crimes in the UK, rather than in the US, on health grounds.
If this is the case, then any guilty verdict is almost certain to result in a more lenient sentence than he would have received in the US, had the extradition gone ahead as planned.
Commenting on this latest development in the long-running saga, Graham Cluley, senior technology consultant with Sophos, said in his blog that it could be "viewed as a ray of light in an otherwise gloomy outlook for McKinnon's many supporters, who include members of all the major British political parties, celebrities".
Earlier this year Sophos polled a number of IT professionals about whether they think he should be extradited, and 71 per cent said they supported McKinnon's cause.