The Iranian authorities are also prepared to allow experts from France, Canada and the United States to examine the data from the boxes, according to the semi-official news agency Tasnim.
Ukrainian International Airlines Flight 752 crashed on 8 January shortly after it took off from Tehran’s international airport killing all 176 people aboard.
After initially denying responsibility, Iran’s elite Revolutionary Guards (IRGC) admitted they had mistaken the jet for incoming fire and took it down with anti-aircraft missiles.
The fate of the black boxes, which hold vital information of the aircraft’s final moments, remained unclear after Iran refused to hand it over to Boeing, the American company which made the jet.
"With the use of the expertise of the countries of France, Canada and America we will try to read the (flight data recorder) in Kiev," Hassan Rezaifar, a director in charge of accident investigations at Iran's Civil Aviation Organisation was quoted as saying.
"If this effort is unsuccessful then the black box will be sent to France."
The black boxes will not be read in Iran, Mr Rezaifar added.
Hours before Flight 752 took off at 06.13am (03.13 GMT), Iran had fired a volley of ballistic missiles at airbases in Iraq housing US troops.
Tehran’s strikes were retaliation for an American drone strike on Baghdad International Airport which killed Iranian top general Qassem Soleimani.
Amid the heightened tensions, a garrison near Tehran's airport mistook Flight 752 for possible incoming fire from the States.
All 176 onboard including the crew and 15 children were killed in the crash. Among the dead were 82 Iranians, 63 Canadians, 11 Ukrainians, 10 Swedes and four Britons.
Prime minister Justin Trudeau, who has been pressing for a full investigation into the plane downing, said on Friday that Tehran should send the black boxes to France for analysis.
He added that France was one of the few countries with the ability to read the flight and cockpit data recorders from the jet, which he said were badly damaged.
Iran has faced a deepening crisis abroad and at home over the plane disaster.
Protesters have taken to the streets in recent days demanding the overthrow of the authorities over the incident. It follows months of rallies that first erupted over sharp fuel price hikes and have been violently put down by the police.
On Friday, under pressure Iran's supreme leader Ayatollah Ali Khamenei threw his support behind the IRGC in his first Friday sermon since 2012.
He told worshippers that the elite Guards could take their fight beyond Iran's borders over the killing of Soleimani.
"Our enemies ... were happy that they found an excuse to undermine the Guards, the armed forces and our system," Khamenei said in his sermon, heaping praise on the Guards for protecting Iran.
Khamenei said Soleimani's work of projecting Iran's military influence abroad would continue and said the Quds Force he commanded "protects oppressed nations across the region."
He said Quds Force soldiers were "fighters without borders".
Agencies have contributed to this report