Former US serviceman, Jordan Matson, posted an entry on Facebook, indicating that the dead Briton was a former Royal Marine.
"I lost a brother very close to me…from the United Kingdom and former royal marine gave his life combating terrorism for his nation and Kurdistan," the post said.
However, the commander of the Kurdish Protection Unit YPG confirmed the news to a BBC journalist.
The identity of the killed has not been disclosed for ethical reasons, as the family of the volunteer had not yet been notified, IBT said.
In February, dozens of Western volunteers were reported to have travelled to Iraq and northern Syria to join Christian Assyrians and Kurdish forces in the fight against ISIL militants, which have been operating in Syria since 2012.