Fazlullah is believed to have ordered the failed 2012 assassination of Malala Yousafzai, who became a global symbol of the fight for girls' rights to schooling, and who later won the Nobel Peace Prize.
US forces conducted a counterterrorism strike on Thursday in eastern Kunar province, close to the border between Afghanistan and Pakistan.
But the Pentagon would not confirm Fazlullah's death, as it can take time to gather definitive proof. Top militant leaders have been reported dead before -- only to later resurface.
"We targeted (Fazlullah) but we're not ready to call jackpot yet," a US defense official told AFP.
A second defense official also confirmed the strike had targeted Fazlullah.
Afghanistan's defense ministry spokesman said Fazlullah was among those killed in the strike.
"I can confirm that the TTP leader Fazlullah was killed in a joint Afghan and US operation in Kunar on Thursday," Mohammad Radmanesh said, using the group's Urdu name, Tehreek-e-Taliban Pakistan (TTP).
There was no official confirmation from Pakistan, but a Pakistani senior security source told AFP that Fazlullah is believed to have been killed.
The US State Department in March announced a $5 million reward for help locating Fazlullah, who has been linked to bloody attacks in Pakistan and the 2010 attempted Times Square car bombing in New York.
It said the group has "demonstrated a close alliance with Al-Qaeda" and had given explosives training to Faisal Shahzad, the would-be Times Square bomber.
Fazlullah's group was behind the massacre of more than 150 people at a Peshawar school in December 2014, and nine dead in another attack in December 2017 in the same city.
According to Pakistani officials, Fazlullah, who is believed to be in his 40s, took refuge in Afghanistan after the TTP was pushed out of Pakistan following multiple offensives by the military on its safe havens.
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