The commander, Khan Sayed, led a breakaway faction of the Pakistani Taliban.
The drone strike occurred on Wednesday in the Damma region in Khost province, near Pakistan's town in North Waziristan, Pakistani intelligence officials said. They said the strike killed 12 militants and injured 20 others.
However, Sayed's death is yet to be officially confirmed.
According to witnesses, Taliban commanders were meeting to resolve disputes when the drone strike took place.
"Sajna was a leading figure of the Pakistan Taliban," said a senior Pakistani military official said.
"Both Pakistani security forces and Americans were after him for a long time."
If the commander's death is confirmed, "it would certainly be a big blow to the Taliban, both in Pakistan and Afghanistan," a Pakistani Taliban commander said.
In 2014, Sajna publicly rejected the Pakistani Taliban's leader, Maulana Fazlullah, and said his faction would continue to fight on its own. The feud erupted after an American drone strike killed Fazlullah's predecessor, Hakimullah Mehsud.
Sajna said in a statement that he was leaving because "the present leadership has lost its path."