The 29-year-old, a kick-boxer, joined the IS in January.
According to the media, he last month spoke for TV SRT to say he was "trying to build a modern caliphate state in Syria."
"If I die doing good, I will certainly be happy," said Gashi at the time.
The local media in Pristina are quoting Swiss media to report that Gashi was killed on June 27 - something announced on Facebook by his brother.
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