All 176 people on board the plane were killed when the Ukrainian International Airlines flight was shot down on January 8 shortly after takeoff from Tehran en route to the Ukrainian capital, Kyiv.
"With the use of the expertise of the countries of France, Canada and America we will try to read the [flight data recorder] in Kyiv," Hassan Rezaifar, a director in charge of accident investigations at Iran's Civil Aviation Organization, was quoted as saying by the news agency.
"If this effort is unsuccessful then the black box will be sent to France."
Ukraine's Foreign Minister Vadym Prystaiko confirmed the news, saying it was "consistent with international standards, although we still demand that they be given to us immediately to ensure the independence and objectivity of the investigation."
After initial denials, Tehran admitted it shot down the plane "unintentionally" while on high alert after firing missiles at US troops stationed in Iraq in retaliation for the killing of top Iranian commander Qassem Soleimani by a US strike in Baghdad.
Prystaiko told CNN on Wednesday that Kyiv has "good cooperation" with Tehran on the crash investigation, but lacked "access to the information stored in the black boxes".
"We just want to know that nobody will be tampering with the recordings themselves," he said.
Prystaiko said an Iranian official will visit Kyiv next week "to apologise officially and provide explanations".
On Thursday, Canada, Ukraine, Sweden, Afghanistan and the United Kingdom issued a five-point plan for cooperation with Iran during the investigation, calling for "full and unhindered access" for foreign officials.