Al Banna, also known as Abu Ayman Al Masri, is the last surviving founding member of Al Qaeda in the Arabian Peninsula (Aqap), the US State Department said.
He was its chief of security and provided military and security guidance.
“In a 2010 article for Aqap’s English-language online magazine, Al Banna described the September 11, 2001 terrorist attacks on the United States as virtuous and threatened to target Americans worldwide in response to US actions overseas,” the State Department said.
It appealed for information on Al Banna through its Rewards for Justice programme on Thursday.
The US officially designated Al Banna as a terrorist in June 2017.
The State Department said Aqap, which was designated as a terrorist group in 2010, has taken aim at local, US, and western interests in the Arabian Peninsula, as well as abroad.
The group has claimed responsibility for a number terrorist attacks, including the January 2015 assault on the offices of satirical newspaper Charlie Hebdo in Paris that killed 12 people.
Before joining Aqap, Al Banna was a leader of the Egyptian Islamic Jihad group in Yemen from 1996 to 1998 and was in charge of training and intelligence operations.
He is believed to have planned the 1993 assassination attempt on former Egyptian prime minister Atef Sedky before fleeing to Yemen and joining Al Qaeda.
Al Banna has survived repeated US attempts to kill him with missiles fired from drones.
In October 2011, the Pentagon claimed that he was killed with six other people, but this proved to be wrong.
Al Qaeda remains active in Yemen, and is suspected to have carried out the attack on a security post in the south in September that led to the deaths of at least 21 Yemeni troops.