Berisha, 34, served two-thirds of his prison sentence before being recently expelled from Switzerland, Tages Anzeiger reported on Monday.
The newspaper said it is not clear whether he will serve further time in Kosovo.
He was convicted of killing a 26-year-old Macedonian in a spat about a place to park in Dübendorf in the canton of Zurich one evening in February 2005.
After the attack, Berisha fled the scene before being arrested during a road check in the Peja region of Kosovo on October 16th 2005.
Switzerland subsequently issued a request for his extradition to be tried for murder.
He was convicted in August 2009 and an appeal was rejected in 2011.
Berisha, who was living in Winterthur, had already served time in jail for striking police officers, according to the report.
He was the Swiss junior Thai boxing champ in the late 1990s.
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