Khamis, 27, who runs the feared Khamis Brigade that has been prominent in its role of attacking rebel-held areas, is said to have died on Saturday night, according to media reports.
According to reports on Algerian TV, a Libyan air force pilot crashed his jet into the Bab al-Aziziya compound in Tripoli in a kamikaze attack.
Khamis allegedly died of burns in hospital. The Gaddafi regime has denied the reports.