"The initiative to the British government is to release its citizen Stephen Malcolm, who also has South African nationality, if it deports Abu Qatada to one of the 'Arab Spring' countries," said the statement, which could not be verified, from Al Qaeda in the Islamic Maghreb (AQIM).
"If Britain ignores this offer it will bear the consequences of handing Abu Qatada to the Jordanian government," it added.
Egypt, Tunisia, Libya and Yemen have seen changes of leadership after uprisings last year known as the Arab Spring. The revolts have empowered Islamists who were often persecuted by previous governments.
Malcolm is thought to be one of nine Europeans, including six French nationals, seized by the al Qaeda branch in Mali and Niger since September 2010. It said in January it would kill them if France and its allies attack its bases in northern Mali.
The group has said the others are from Sweden and Holland.
Africa's Sahel region has become a haven for al Qaeda-linked operatives taking advantage of the vast and lawless area, and is believed to have raked in millions of dollars in ransoms. Mauritania's army has launched a series of attacks on AQIM bases inside Mali in recent months.
Britain said this month it would resume plans to deport Abu Qatada to Jordan, where he has been convicted in absentia of involvement in militant plots.
The Jordanian preacher had been under virtual house arrest at his home in London since February, when he was freed from a British prison after a court said his detention without trial was unlawful.
The European Court of Human Rights ruled in January that he would not receive a fair trial in Jordan because evidence against him might have been obtained through the use of torture, though London says it has received assurances of a fair trial.
Under the deal struck with Jordan, Abu Qatada would be tried by a court used to hearing criminal cases and not a quasi-military body. The case would be heard in public with civilian judges and his conviction in absentia would be quashed.