Arrai Television, a pro-Gadhafi station in Damascus, said Mohammed Abdullah Sanoussi, son of Abdullah Sanoussi, Gadhafi's head of security and brother-in-law, was killed at the same time, the Los Angeles Times reported Monday.
Khamis Gadhafi was believed to be 28, the report said. He commanded the 32nd Brigade, which had been given the responsibility of defending Tripoli.
As the rebels approached Tripoli in August, allies in the city rose in revolt. Many of Gadhafi's soldiers, including those in the 32nd Brigade, put down their weapons and shed their uniforms.
Human rights groups have accused the 32nd Brigade of wholesale killing of prisoners in the final hours before Tripoli fell.
Gadhafi's whereabouts are unknown. One of his surviving sons is in Niger, two fled to Algeria and two others are missing. Another was reported by the regime to have been killed in April by a NATO airstrike on Tripoli.