Pentagon officials said they had no immediate information on such a strike or of al-Baghdadi being wounded.
Iraq’s Defence and Interior Ministries issued statements saying al-Baghdadi had been wounded, without giving further detail.
An Interior Ministry intelligence official said al-Baghdadi was hit during a meeting on Saturday with militants in the town of Qaim in Iraq’s western Anbar province.
The official, citing informants within the militant group, said the strikes wounded al-Baghdadi. A senior Iraqi military official also said he learned in operational meetings that al-Baghdadi had been wounded.
Neither knew the extent of al-Baghdadi’s apparent injuries.State television later also reported that al-Baghdadi had been wounded.
Al-Baghdadi, an ambitious Iraqi militant believed to be in his early 40s, has a $10m (£6.2m) bounty on his head.
Since taking the reins of the group in 2010, he has transformed it from a local branch of al-Qaida into an independent transnational military force, positioning himself as perhaps the pre-eminent figure in the global jihadi community.
A US-led coalition has been launching air strikes on “Islamic State” (IS) militants and facilities in Iraq and Syria for months as part of an effort to give Iraqi forces the time and space to mount a more effective offensive. IShad gained ground across northern and western Iraq in a lightning advance in June and July, causing several of Iraq’s army and police divisions to fall into disarray.
On Friday, US President Barack Obama authorised the deployment of up to 1,500 more American troops to bolster Iraqi forces, including into Anbar province, where fighting with IS militants has been fierce. The plan could boost the total number of American troops in Iraq to 3,100.
Meanwhile, a married father-of-two is believed to have become the second British jihadist to have killed himself while fighting in Syria and Iraq.
The man, named in reports as Kabir Ahmed, from Derby, is believed to have been involved in a suicide bomb attack in the town of Beiji, north of the Iraqi capital Baghdad, two days ago.
Going under the name Abu Sumayyah, the 32-year-old is said not to have told his family that he was fleeing Britain to fight for IS.
It would make Ahmed the second British jihadist suicide bomber, after Abdul Waheed Majeed – a 41-year-old father-of-three from Crawley in West Sussex – blew himself up in February when he drove a lorry laden with explosives into a jail in the Syrian city of Aleppo.
The Foreign Office is now looking into the incident. A spokesman said: “We are aware of reports of the death of a British national in Iraq.”
Ahmed was one of three men to be jailed in 2012 for handing out a leaflet calling for gay people to be executed.
In July, BBC Panorama broadcast an interview with Ahmed in which the Briton confessed to being a jihadist with IS fighting in Syria. He said: “Everybody has got their name on the list (to become a suicide bomber) and everyone is forcing the Amir to push their name up. Everyone wants to fight for the sake of Allah.
“If the British Government commits terror against our people, is unjust towards our people, kills and murders and rapes our people then you can expect attacks on your soil.”