The house appeared to have been damaged in fighting.
Saleh on December 2 announced the end of his alliance with the Iran-backed Huthi rebels, with whom he has jointly ruled the capital, Sanaa, for three years.
The rift appeared to be part of a plan by the Saudi-led coalition, which was fighting against the Houthis, to turn the tide of the war in their favor.
Saleh had on Saturday issued his message to the Saudi-led coalition in a speech broadcast from the studios.
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 Interior Ministry, affiliated with the Houthis, said that Houthi-allied security forces are carrying out raids and arrests at the homes of Saleh's associates and supporters.
"The president will soon announce a general amnesty for all those who collaborated with the Houthis in recent months and who have retracted that allegiance", Prime Minister Ahmad Obaid bin Daghr said.
The United Arab Emirates (UAE) dismissed claims that Yemen's Houthi rebels fired a missile towards a nuclear plant in Abu Dhabi on Sunday, state news agency WAM reported. Iran supports the Houthis but denies arming them.
Saleh also called for a joint ceasefire between his allies and Houthi rebels, and the Saudi-led coalition, which has been at war with the impoverished country since March 2015. Residents and medics told Reuters at least 125 were killed in the fighting on Monday, according to Reuters.
Tribal sources in Saleh's hometown Sanhan, south of Sanaa, on Monday reported intense overnight fighting between the Houthis and Saleh loyalists.
The Houthis have also seized the homes of Saleh and some of his family members in a southern district of Sanaa - the so-called Political District - which witnessed some of the heaviest clashes. But he recently switched his alliance to Saudi Arabia, which has led a three-year bombing campaign against the Houthis in Yemen and implemented a blockade of Yemeni ports.
That dealt a serious blow to his already fragile alliance with rebel chief Abdul Malik al-Houthi.
Yemen's war has killed more than 10,000 people since 2015, displaced more than two million people, and caused a cholera outbreak infecting almost one million people.
Global aid groups warned on Monday they were losing the ability to reach civilians in Sanaa.