Mr McKinnon faces 60 years in jail if convicted in the US
The new home secretary has been urged to overrule her predecessor's decision to allow the extradition of UK computer hacker Gary McKinnon.
Mr McKinnon's lawyers have made "representations" to Conservative Theresa May as part of a long campaign to prevent a US trial for their client.
A judge is due to rule on whether the previous home secretary Alan Johnson was wrong to allow the extradition.
Both David Cameron and Nick Clegg have previously criticised the move.
The new Foreign Secretary William Hague has not commented on this specific case but has promised a fresh look at extradition arrangements between the UK and the US.
Glasgow-born Mr McKinnon, who has Asperger's syndrome, is accused of breaking into the US military computer system. He says he was seeking evidence of UFOs.
The computer systems Mr McKinnon is accused of breaking into include those at the Pentagon. If convicted, the 44-year-old - now of Wood Green, north London - faces 60 years in prison.
Mr McKinnon's lawyer Karen Todner said the solicitors firm Kaim Todner had asked Mrs May to "intervene and prevent the extradition".
"We hope the new Liberal-Conservative Government will act upon their previous public statements that it would be unjust to extradite Mr McKinnon," she said.
Last year, Mr Cameron said that if Mr McKinnon had questions to answer there was "a clear argument to be made that he should answer them in a British court".
In January Mr McKinnon's legal team was granted permission for a judicial review of Mr Johnson's decision that sending him to the US for trial would not breach his human rights.
At the time the Home Office said it had "noted" the court's decision.
Liberal Democrat leader Nick Clegg said the judicial review was "heartening news" and said he hoped the courts would "display more courage than our ministers".
Mr McKinnon's mother, Janis Sharp, has often spoken of the stress of the long campaign.
Speaking earlier this year she said: "We've fought for so long for compassion and understanding. Gary's health has badly declined, it's been traumatic to see."
Earlier this month she stood for election as an independent in Jack Straw's Blackburn constituency, saying she blamed the justice secretary for pushing through the extradition treaty with the US.
She came last with 173 votes.