Sheikh Aweys used to head an Islamic armed group
Somalia's Islamic courts, which control Mogadishu, have set up a new power structure in which a top Islamist wanted by the US is to play a key role.
Sheikh Hassan Dahir Aweys - on the US list of terrorists with alleged links to al-Qaeda - is to head an 88-strong legislative council, or parliament.
A new, eight-member executive committee, or cabinet, will be chaired by a moderate, Sharif Sheikh Ahmed.
Discussions on the new structure are still under way in the capital.
Mr Ahmed is chairman of the Union of Islamic Courts, which wrested control of Mogadishu from warlords two weeks ago.
The new legislative council is to take decisions, which will be then be implemented by the executive committee.
The new posts have not been formally announced and correspondents say there is a struggle for control between the radicals and the moderates.
Sheikh Aweys, a prominent cleric, is seen as more radical. He previously headed an armed group, al-Itihaad al-Islamiya, which the US said had links with al-Qaeda.
The network of 11 Islamic courts has been set up in recent years in Mogadishu, funded by businessmen in an attempt to re-establish law and order.
The courts' stated goal is to restore a system of Sharia law and put an end to impunity and fighting.
An interim government based in Baidoa, 200km (125 miles) north of the capital, Mogadishu, has been largely ineffective.
The US is widely believed to have backed the defeated warlords, as part of its war on terror.
It has neither confirmed nor denied the reports but says it will support those working to prevent "terrorists" from setting up in Somalia.
Last week, a senior US official urged the Islamic courts to hand over three men it wants in connection with previous attacks in East Africa, blamed on al-Qaeda sympathisers - the 1998 bombings of US embassies in Kenya and Tanzania and the 2002 attacks on Israeli tourists in Kenya.