Details of Hamza Bin Laden's place or date of death remain unclear in the anonymously-sourced reports.
In February, the US government offered $1m for information leading to his whereabouts.
Hamza Bin Laden, thought to be aged about 30, had released audio and video messages calling for attacks on the US and other countries.
The reports were first carried by NBC and the New York Times.
US President Donald Trump refused to comment on the issue when asked by reporters on Wednesday, as did the White House national security adviser John Bolton.
Hamza Bin Laden urged jihadists to avenge his father's killing by US special forces in Pakistan in May 2011.
He had also called on the people of the Arabian peninsula to revolt. Saudi Arabia stripped him of his citizenship in March.
A son brought up to hate America
It's a sign of how little is known about Hamza Bin Laden that US officials were never able to definitively confirm his age.
In recent months they had floated suggestions that he may have been in Afghanistan, Pakistan or Iran. But they couldn't even say for sure in which country one of America's "most wanted" was hiding.
The million dollar price tag for information was a measure not just of the potential danger he posed but also his symbolic importance to al-Qaeda and its propaganda machine.
Hamza was only a child when his father helped plotted the 9/11 attacks but, according to the extremist group's legend, he was by his side at the time.
For a son brought up to hate America, avenging his killing at the hands of special forces was always going to be an obsession. In recent years he sent online messages calling for attacks against the United States and its allies.
Hamza Bin Laden's death, if officially confirmed, will silence someone who was emerging as a new voice of Al Qaeda. However it will not end the threat from an organisation that carried out the world's most notorious terror attack.
Al-Qaeda: The basics
Emerged in Afghanistan in the late 1980s, as Arab volunteers joined US-backed Afghan mujahideen fighting to expel the occupying Soviet forces
Osama Bin Laden set up an organisation to help the volunteers, which became known as al-Qaeda, or "the base"
He left Afghanistan in 1989, returning in 1996 to run military training camps for thousands of foreign Muslims
Al-Qaeda declared "holy war" on Americans, Jews and their allies