Al-Qaeda in the Islamic Maghreb (AQIM) has offered to free a British-South African hostage if the UK government allows the cleric Abu Qatada to choose a country for his extradition, the SITE monitoring service says.
AQIM also threatened that Britain would "open the door of evil" to its country and people should it send the imam back to his native Jordan where he faces jail, the report from the US-based organisation said.
Al-Qaeda's North African franchise has been holding Stephen Malcolm and two other Western men hostage since abducting them last November in the northern Mali desert city of Timbuktu.
Britain has been trying to deport Abu Qatada to Jordan for more than six years, arguing he is a threat to national security. The cleric was convicted in Jordan in absentia in 1998 over his involvement in terrorism attacks.
But his removal has in the past been blocked by the European Court of Human Rights, which cited the risk that evidence obtained from torture would be used against him on his return to Jordan.
The court is now considering the latest appeal by the cleric.
The SITE report said AQIM had offered a deal, "to release a hostage if the British government allows radical cleric Abu Qatada al-Filistini the opportunity to choose a country for his extradition".
The group had declared on internet forums on Sunday "that it has followed Abu Qatada's case for years".
The other hostages taken on November 25 were Nils Joan Viktor Gustafson, a Swedish national, and Jacobus Nicolo Ruke, a Dutch national.
AQIM released a picture of the three men in December.