Khamis is a senior figure in the Gaddafi regime and one of its main military commanders.
Zlitan is a frontline town where some of Gaddafi’s most loyal and best equipped troops are making a stand to defend the approaches to Tripoli, 160km away.
A Nato official at operations headquarters in Naples said he was aware of the report but could not confirm it.
“We cannot confirm anything right now, because we don’t have people on the ground, but we are trying to find out what we can,” he said.
If confirmed, the death of Khamis Gaddafi would be a severe blow to the leader’s bid to resist a six-month-old Nato-backed uprising and remain in power.
Khamis is head of Libya’s 32nd Brigade, one of Gaddafi’s most professional and loyal units, which has been fighting in Zlitan, which lies between the rebel-held city of Misrata and the capital Tripoli.
The Gaddafi government said earlier this year that a Nato air strike had killed another of Gaddafi’s sons, Saif al-Arab, who had a much lower public profile and no major leadership role.