Hekmatyar is one of the best-known Afghan warlords
A missile was fired from an unmanned Predator spy plane somewhere near Kabul on Monday but missed Mr Hekmatyar, the officials, speaking on condition of anonymity, told several Western news agencies.
The CIA has refused to comment but a Pakistan-based news agency confirmed a missile attack was carried out on Monday in the Shegal Gorge in Konar Province and said 30 people were wounded.
The whereabouts of Mr Hekmatyar have been a mystery since Iran announced it had expelled him in February after he condemned the US presence in Afghanistan and the Afghan interim government.
"I believe some others were killed in the strike but the target escaped," an unnamed senior US official was quoted as saying by the Reuters news agency.
According to the US sources, a Hellfire anti-tank missile was used in the attack.
The Afghan Islamic Press said in its report that the Shegal Gorge was controlled by a former ally of Mr Hekmatyar, named as Kashmir Khan.
Mr Khan is now a member of the Northern Alliance and a supporter of the interim government administration, the agency added.
'Serious threat'
An unnamed official in the Bush administration told the news agency that Washington had "serious concerns" regarding Mr Hekmatyar, his views and his possible contacts with the ousted Taleban regime and al-Qaeda militants.
A US official quoted by the French news agency AFP said Mr Hekmatyar and his radical Hezb-i-Islami party had offered rewards for the deaths of US troops in Afghanistan and had attacked forces of the interim government.
"We're not engaged in entering disputes among the various factions on the ground," the official said.
"But when people threaten the lives of US troops and encourage people to cause them harm we take that seriously."
President George W Bush said this week that the US was prepared to "go after individuals in the theatre of war" if they intended to "do harm to America".
Opposition figure
A senior member of Hezb-i-Islami based in Peshawar, Pakistan, has confirmed that Mr Hekmatyar is back in Afghanistan.
"Hekmatyar is somewhere in Afghanistan but we don't know in which area he is living," Qutbuddin Hilal told the Associated Press.
The warlord's supporters, who gained notoriety for the bloody siege of Kabul during the post-Soviet civil war, have been accused by interim government officials of planning a coup.
Security forces carried out mass arrests in Kabul in April, saying Hezb-i-Islami was planning bomb attacks.
A spokesman for Mr Hekmatyar denied his involvement but the warlord, who served briefly as Afghan prime minister before the Taleban came to power, has dismissed Hamid Karzai's US-backed administration as a puppet regime.
"While foreign troops are present, the interim government does not have any value or meaning," the warlord told Reuters in an interview in February.
"We prefer involvement in internal war rather than occupation by foreigners and foreign troops."