Houthi-controlled al-Masirah TV cited Houthi officials as announcing the “end of the crisis of the treason militia and the killing of its leader”.
There was no independent confirmation, but pictures circulated on social media appeared to show Mr Saleh’s body.
His political party earlier denied that he was dead after Houthi fighters blew up his house in the capital, Sanaa.
Until last week, Mr Saleh’s supporters had been fighting alongside the Houthis in a war against Yemen’s current President, Abdrabbuh Mansour Hadi.
More than 8,670 people have been killed and 49,960 injured since a Saudi-led coalition backing Mr Hadi intervened in the conflict in 2015, according to the UN.
The conflict and a blockade by the coalition has also left 20.7 million people in need of humanitarian aid, created the world’s largest food security emergency, and led to a cholera outbreak that is thought to have killed 2,211 people since April.