The Lebanese daily As-Safir was the first to break the news, saying the two were detained about 10 days ago near a border crossing point with Syria. It said the arrest was in "coordination with foreign intelligence agencies."
The two were carrying fake identification cards, the Associated Press reported, adding that the woman is being questioned.
French newspaper Le Monde described al-Baghdadi, formerly a longtime leader of al-Qaeda in Iraq, as "the new Bin Laden". The United States has a $10 million bounty on his head.
Now based in Syria, al-Baghdadi, also known as Abu D`ua, has taken personal credit for a range of attacks in Iraq on both state security forces and ordinary citizens since 2011.
In July, a video surfaced of a man officials believe to be al-Baghdadi addressing a crowd from a mosque balcony in Mosul. The Iraqi city is home to some 2 million people, and is part of a territory that includes parts of Iraq and Syria that the Islamic State, also known as ISIL or ISIS, has declared to be its own Islamic state, or caliphate.
Little is known about al-Baghdadi`s personal life, including how many wives and children he has. Conservative interpretations of Islam allow for a man to marry up to four wives.
Al-Baghdadi`s first wife is believed to be Iraqi citizen Suja al-Dulaimi, who was reportedly held by Syrian authorities and freed in a prisoner exchange with al-Qaida`s branch in Syria earlier this year.
In March, the Nusra Front freed more than a dozen Greek Orthodox nuns, ending their four-month captivity in exchange for Syrian authorities releasing dozens of female prisoners.
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