The Iranian authorities are also prepared for experts from France, Canada and the United States to examine the data from the boxes, it said.
All 176 people aboard the plane were killed when the Ukrainian International Airlines flight was shot down on January 8, shortly after take-off from Tehran en route to the Ukrainian capital Kiev.
"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 by Tasnim.
"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 said, according to Tasnim.
Fifty seven of the dead were Canadian. Prime Minister Justin Trudeau, who has been pressing for a full investigation into the plane downing, said on Friday that Iran should send the black boxes to France for analysis.
He said Iran does not have the expertise or equipment needed to look at them, but that France has a lab that can do it.
The spokesman for the French accident investigating bureau, or BEA, had said it had no information about eventually obtaining the demolished plane's black boxes, the voice and data recorders, to decipher them.
Sebastien Barthe had added that it is up to Iran, which is in charge of the investigation, to decide the matter.
Iran has faced a deepening crisis abroad and at home over the plane disaster, with authorities taking several days to announce that its military had accidentally shot the plane down.
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The downing occurred as Iran was on high alert for possible retaliatory action following its strikes on Iraqi bases housing U.S. troops.
Those strikes were in revenge for the U.S. killing of top military commander Qasem Soleimani in a drone attack in Baghdad on January 3.