The Yemen-based Al-Qaeda in the Arabian Peninsula (AQAP), classified by the United States as the network's deadliest franchise, said the two men were "heads of evil".
"In support of the jihad of our Muslim brothers in Yemen," AQAP said it was offering a "reward of 20 kilograms (44 pounds) of gold to whoever kills or captures" Saleh or Huthi.
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It posted the pictures of both leaders, who belong to the Zaidi sect of Shiite Islam -- a minority in Yemen where almost 70 percent of the population is Sunni.
The offer came as a Saudi-led coalition of nine Arab, mostly Sunni states, completed its second week of air strikes against Shiite Huthi rebels and their allies, troops loyal to Saleh.
Huthi is believed to be based in the northern Shiite stronghold of Saada. But the whereabouts of Saleh, three years after he resigned following an Arab Spring-inspired uprising, remain unknown.
As fighting rages on the ground between rebels and forces of President Abedrabbo Mansour Hadi, AQAP last week seized much of Hadramawt provincial capital Mukalla in southeastern Yemen.