Last week, McKinnon, who suffers from Asperger's syndrome, looked set to face trial in the US after Johnson said there were no grounds to prevent his extradition. After considering the evidence presented to him, Johnson said that sending McKinnon to the US would not breach his human rights.
However, Johnson said yesterday he was considering an appeal by McKinnon's lawyers to extend the seven-day period they have to apply for judicial review.
"As I have said at every stage of these proceedings, we will not commence extradition proceedings until all legal avenues Mr McKinnon wants to pursue have been exhausted," Johnson told the House of Commons.
McKinnon's legal battle dates back to 2001, after he broke into US military computers, including those belonging to NASA, in a bid to prove the US government had knowledge of UFOs.
While he says his actions caused no damage, the US claims he stole 950 passwords, deleted files at a naval base in New Jersey and rendered the military computer networks used following September 11 useless. The US estimates the damage caused by McKinnon at $700,000 (£433,000).
In August 2008, the European Court of Human Rights agreed to allow McKinnon to be extradited to the US. In a bid to avoid extradition McKinnon told the British Crown Prosecution Service (CPS) said he would plead guilty if tried in the UK. However in February this year, the CPS refused to bring charges against McKinnon.