British Home Secretary Theresa May customarily makes decisions on extraditions within two months, but Tuesday marked the passing of that deadline.
Aldhouse, 29, has been accused of the brutal knifing of a former US Marine, Dashawn Longfellow, on Phuket in August last year.
A court in Britain decided on June 30 that there were no grounds for denying the reqest from Thailand for Aldhouse's extradition.
However, it is believed some concerns remain about the state of the jails in which Aldhouse would be held in Thailand.
Overcrowded conditions at Phuket prison and in other Thai jails do not conform to international standards.
Aldhouse, accused of ambushing Longfellow after losing a fist fight at a local Phuket bar in the southern resort of Rawai, fled Phuket and reached London's Heathrow Airport before being arrested.
A decision by the Home Secretary in favor of an extradition would probably be followed by an appeal by Aldhouse to Britain's High Court against the move.
A decision by the Home Secretary against the extradition on the grounds of conditions in Thai jails would in all likelihood trigger further debate about the three Britons being held in Phuket Prison, and others in jails elsewhere in Thailand.
Thailand would almost certainly appeal a decision against extradition.
Either way, Aldhouse is unlikely to reappear on Phuket before the second anniversary of the murder.
News Analysis With the first anniversary of the brutal knife murder of an American visitor just weeks away, questions are being asked his alleged killer and Phuket's crowded jail.
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Hope the psycho rots for the rest of his life in the Bangkok Hilton. With less than an hour of physical exercise a day, he won't be so butch for much longer.
Posted by Graham on August 31, 2011 15:00