High court judges Lord Justice Stanley Burnton and Mr Justice Wilkie will hear an application for a judicial review on 14 July, according to reports.
McKinnon, accused of the "biggest military hack of all time" by the US, faces a stretch of up to 60 years in a maximum security prison if extradited, according to his solicitor.
His MP (Tory David Burrowes) today called for further debate on whether McKinnon's diagnosis with autism should have a bearing on the case.
In the Commons, he said: "My constituent Gary McKinnon, the computer hacker, has been diagnosed with Asperger's Syndrome.
"Yet the previous Home Secretary has chosen to disregard the impact of his condition and has approved his extradition to the United States."
The long-running case continues.