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.
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