The incident that also killed three others from Bhittani's group, took place near Darga Mandi area of Ghulam Khan town in the tribal region, Dawn online reported citing its sources.
The TTP has so far not confirmed Bhittani's death.
Bhittani served as the acting TTP chief after Hakeemullah Mehsud's death and also headed the Taliban supreme shura.
He hails from the Khichi sub-tribe in Waziristan and was known for his ruthless predisposition towards those taken as prisoners by the TTP.
In Dec 2011, Bhittani's group overran the military bastion, killed an officer and kidnapped 23 other soldiers. Their mutilated bodies with 40 bullet holes each and signs of torture were later recovered from North Waziristan region.
North Waziristan is one of seven regions in Pakistan's Federally Administered Tribal Area governed by tribal laws.