Said al-Shihri, described as the second-in-command of al-Qaeda in the Arabian Peninsula (AQAP), has been killed in an operation in southern Yemen, government officials say.
Al-Shihri was reportedly killed with six others in the Hadramawt area.
Some reports say Yemeni troops were involved, others that it was an air strike, possibly a US drone attack.
Al-Shihri was a Saudi national who was released by the US from detention in Guantanamo Bay in 2007.
The Yemeni army has been fighting Islamist militants in the south for months.
The Yemeni ministry of defence website said al-Shihri was killed along with six other militants in an operation, but gave few details.
Official sources in Yemen told the BBC the death occurred in an air raid in the Wadi Ain area of Hadramawt.
Military sources, however, said they had no information on the death and refused to confirm it. But the sources did confirm the area was subject to air raids.
It is not the first time that Said al-Shihri has been reported killed, but if confirmed it would be an important scalp for the Yemeni government in its US-backed campaign against al-Qaeda.
Since Abdrabbuh Mansour Hadi became president in February, that fight has intensified - with major gains made in driving al-Qaeda and Islamic extremists linked to the group out of towns they had seized in southern Yemen.
Al-Shihri himself is a well-known figure. He was detained in Guantanamo Bay for many years after being captured in fighting in Afghanistan. But he was released back to his native Saudi Arabia in 2007. He went through a Saudi rehabilitation programme for Islamic militants.
But his decision two years later to go to Yemen to join al-Qaeda's jihadist fight raised questions in the US about the risks of releasing prisoners from Guantanamo back to their home countries. Since then, al-Shihri is reported to have been involved in the kidnapping of foreigners in Yemen.
Separate Yemeni sources said another Saudi and an Iraqi national were among the other people killed in the operation, which took place last Wednesday.
Yemeni defence ministry officials told Associated Press that the militants killed were travelling in a car and that it was hit by a missile believed to have been fired by a US drone, although this has not been confirmed.
Other reports say the operation was carried out by the Yemeni military.
US cables released by the Wikileaks website last December suggested that Yemen had allowed secret US air strikes against suspected al-Qaeda militants.
Then-President Ali Abdullah Saleh claimed the raids were conducted by Yemen's military when they were in fact carried out by the US, according to the cables.
AP quoted a senior official at President Abdrabbuh Mansour Hadi's office as saying that DNA tests had not yet confirmed al-Shihri's identity.
Al-Shihri was said to have escaped a US drone attack on 20 September last year on the village of al-Mahfad in Abyan province.
He was released from Guantanamo Bay in 2007 and had been sent to Saudi Arabia for rehabilitation.
The US has labelled AQAP the most dangerous branch of al-Qaeda.
AQAP was formed in January 2009 by a merger between two regional offshoots of the international Islamist militant network in Yemen and Saudi Arabia.
Al-Qaeda in the Arabian Peninsula
- Formed in January 2009 by a merger between al-Qaeda in Saudi Arabia and Yemen
- Based in eastern Yemen
- Led by Nasser al-Wuhayshi, a Yemeni former aide to Osama Bin Laden
- Aims to topple Saudi monarchy and Yemeni government, and establish an Islamic caliphate
- Came to prominence with Riyadh bombings in 2003, and 2008 attack on US embassy in Sanaa
- Says it was behind an attempt to blow up US passenger jet in December 2009
It is now led by Nasser Abdul Karim al-Wuhayshi, a former personal assistant to Osama Bin Laden in Afghanistan.
Al-Wuhayshi took over after two earlier leaders, Khaled Ali Hajj and Abdul Aziz al-Muqrin, were killed by Saudi security forces.
The group has claimed responsibility for a number of attacks and has been blamed by US President Barack Obama for attempting to blow up a US passenger jet as it flew into Detroit in December 2009.
In October 2010, the group was accused of sending bombs hidden in two packages addressed to synagogues in the US city of Chicago which were found on planes in Dubai and the UK.
Southern Yemen has been the scene of major clashes between militants and government forces.
The militants took advantage of the uprising that ousted President Saleh in February to take control of large parts of the area.