Information Minister Mahmoud Shammam said fighters had told him they had seen Col Gaddafi’s body, and other officials also said he was dead.
The claims have not yet been independently verified, and other reports said he was captured alive.
The colonel was toppled in August after 42 years in power.
The International Criminal Court has been seeking his arrest.
Nato, which has been running a bombing campaign in Libya for months, said it had carried out an air strike earlier on Thursday that hit two pro-Gaddafi vehicles near Sirte.
It was unclear whether the strikes were connected with the reports of Col Gaddafi’s death.
The head of the National Transitional Council (NTC) Mustafa Abdul Jalil is expected to give a national TV address on Thursday.
Mr Shammam said the NTC leader would officially confirm Col Gaddafi’s death.
“He was killed in an attack by the fighters. There is footage of that,” he said.
Grainy video footage has been circulating among NTC fighters appearing to show Col Gaddafi’s corpse.
AFP news agency reported that the video showed a large number of NTC fighters yelling in chaotic scenes around a khaki-clad body, which has blood oozing from the face and neck.
Another NTC official, Abdel Hafez Ghoga, told AFP: “We announce to the world that Gaddafi has been killed at the hands of the revolution.
“It is an historic moment. It is the end of tyranny and dictatorship. Gaddafi has met his fate.” BBC