The circumstances of Saleh's death were unclear but Houthi officials said their forces caught up with him as he tried to flee capital city Sanaa.
The source said that clashes had renewed on Saturday between the Houthis and Saleh's supporters in the Yemeni capital Sana'a.
The Saudi-led coalition had been fighting both the Shiite Houthi rebels and Saleh's party in Yemen since March 2015 to support the internationally-recognized government led by President Abd-Rabbu Mansour Hadi.
Yemeni President Ali Abdullah Saleh waves to supporters in Sanaa, Yemen, before his ouster in 2011. In a televised interview, Salah also called for resuming relations with Saudi Arabia, if the Saudi-led coalition lifts its blockade of Yemeni ports and air facilities.
"Saleh's actions in Yemen, in working with his former opponents the Houthis, were complicating numerous efforts at resolving the conflict", Harrison Akins, a researcher with the Howard Baker Center, told Newsweek.
In a speech late on Sunday, apparently his last, Saleh formally annulled his alliance with the Houthis.
Saleh, 75, ruled Yemen for more than three decades until his ouster under popular pressure in 2012.
His death and the fighting between his supporters and the Houthis puts the civil war on an unpredictable path.
In this January 3, 2017 file photo, tribesmen loyal to Houthi rebels chant slogans during a gathering aimed at mobilizing more fighters into battlefronts to fight pro-government forces.
Internal rifts have shaken the fragile alliance between the Houthis and Saleh loyalists, who joined ranks in 2014 to seize Sanaa. The rivalry between Riyadh and Tehran, which has increased significantly in recent months, has exacerbated the conflict in Yemen. Yemen is now facing the most significant cholera epidemic in recent history, an outbreak that is especially risky for children.
"Ambulances and medical teams can't access injured, people can't buy food and other supplies", UNICEF's Rajat Madhok said on Twitter. "There is a street war and people are holed up in their houses", according to an activist who works with the International Organization for Migration in Sanaa.
Ex-leader killed by Iranian-backed rebels during attack in Sanaa.