According to an Afghan military commander on Monday, Mulla Abd al-Razzaq Nafis was killed in central Uruzgan province 10 days ago.
Nafis was a close aide to Mulla Umar and a member of the 10-strong Taliban shura (council) formed in June to fight US and Afghan interim government forces.
But the source, Abd al-Razzaq Achakzai, is known to sell attention grabbing “news stories” that have little in common with reality.
Aljazeera’s correspondent in Spin Boldak said Achakzai was particularly well known for selling stories to Reuters which proved to be false.
“Achakzai was the source for the news that nine US soldiers died last week, a story which had no basis in fact whatsoever,” he said.
However, Taliban intelligence officer Mulla Abd al-Samad confirmed he had had no contact with Nafis for two weeks, adding that it was impossible to confirm or deny the death claim.
If Nafis is dead, it will be the second major blow to the Islamist movement in a month.
Taliban’s top military commander in southern Afghanistan, Mulla Abd al-Rahim, was killed on 15 September, though it took two weeks for the organisation to admit his death.
Mulla Umar, whose whereabouts are also unknown, appointed Mulla Wakil Ahmad, elder brother of al-Rahim, as commander of Taliban forces in southern Afghanistan.
Taliban remnants have stepped up attacks in recent months in southern Afghanistan, the former stronghold of the radical Islamist regime ousted from power in late 2001 by US-led forces.
More than 300 people, including aid workers, US soldiers and many Taliban guerrillas, have been killed in violence across Afghanistan since early August.