According to local media reports, Saleh's political party, the General People's Congress, has confirmed his death.
Houthi sources have claimed that the former president was killed by rebels in a rocket-propelled grenade and shooting attack on his car.
A footage circulating on social media appeared to show Saleh's dead body.
However, the images are not verified.
According to a statement read out on Houthi TV, Yemen's interior ministry announced the "killing" of "Saleh and his supporters".
"This is after he and his men blocked the roads and killed civilians in a clear collaboration with the enemy countries of the coalition," it added.
The ministry also said its forces had "taken over all the positions and strongholds of the treacherous militia in the capital, Sanaa, and the surrounding areas, as well as other provinces in order to impose security".
Few local media reports stated that the Houthi rebels had gained control of the majority of the country's capital from Saleh's forces.
However, close sources had denied the reports that Saleh was killed.
Also, the Iranian embassy in Yemen was set ablaze after a mortar shell struck amid the rebel fighting. The Anadolu Agency quoted sources, as saying, that the mortar shell triggered the fire at the embassy premises.
However, it could not be figured out which party was behind the attack on the Iranian embassy.
Both Saleh forces and the Houthi rebels are battling to capture the capital city. The loyalists of Saleh last week had proposed for the talks with the Saudi-led coalition fighting the Houthis to end the three-year conflict in Yemen.
The fighting has claimed more than 10,000 lives since then. The United Nations has described the Yemen conflict as the world's worst humanitarian crisis. (ANI)