They say he died in fighting in Salahuddin province, north of Baghdad. His supporters have denied the claim.
Douri, 72, led the Naqshbandi Order insurgent group, a key force behind the recent rise of Islamic State (IS).
He was deputy to Saddam Hussein, who was ousted when US-led forces invaded Iraq in 2003 and executed in 2006.
Douri was regarded as the most high-profile official of Saddam Hussein's Baath party to successfully evade capture after the invasion, and had a large bounty on his head for years.
He was the King of Clubs in the famous pack of cards the US issued of wanted members of Saddam Hussein's regime after its defeat.
There have been reports of Douri's death or capture before. The now-dissolved Baath party denied the latest claim.
However, al-Arabiya TV showed a picture of what it said was Douri's body.
Salahuddin governor Raed al-Jabouri said he had died during an operation by soldiers and allied Shia militiamen east of Tikrit - a city that was recaptured by the government two weeks ago.
Douri's Naqshbandi Order is the main Baathist insurgent group. Despite its secular roots, it is believed to have played a key role in a major offensive by Islamic State last year.
IS seized swathes of territory in eastern Syria and across northern and western Iraq, in an effort to establish an Islamic "caliphate".
But in recent months Iraqi forces - backed by US-led air strikes since August - have recaptured 25% to 30% of the territory initially lost to IS.
The jihadist group still controls large areas, including the second city of Mosul, in the north
The violence in Iraq has been fuelled by the sectarian divide between Sunni and Shia Muslims.
The government is dominated by politicians belonging to the Shia majority and backed by Shia militias. IS and other insurgent groups are Sunni.
On Friday a car bomb reportedly exploded near the US consulate in Irbil, the capital of the autonomous Kurdish region.