The expected formal announcement later today follows the unanimous vote last week at the UN Security Council to end military operations on October 31.
It came seven months after the Security Council in March authorized "all necessary measures" to protect civilians from attacks by Qaddafi's forces.
The air campaign played a key role in the overthrow of the former longtime leader.
Rasmussen has said that the mission over Libya was "one of the most successful in NATO history."
Libya's new interim authorities declared the country liberated after the capture and killing of Qaddafi and the fall of his hometown of Sirte on October 20.
Rasmussen is scheduled to hold talks today with leaders of the National Transitional Council, who had urged NATO to continue its mission until at least the end of the year.
compiled from agency reports