The US-based monitoring group SITE said Islamic State jihadists claimed a woman described as a "female Zionist soldier" had been captured in the embattled Syrian border town.
Some jihadists said the woman might be Gill Rosenberg, a Canadian-Israeli dual national who had served in the Israel Defense Forces and had volunteered to fight with the Kurds, the monitoring group said.
"The Government of Canada is aware of reports that a Canadian citizen was kidnapped in Syria," a foreign ministry statement said.
The ministry added that it would not "comment or release any information which may compromise ongoing efforts and risks endangering the safety of Canadian citizens abroad."
SITE said jihadists were discussing on the Internet whether the woman should be executed or traded for Muslim prisoners.
IS jihadists began advancing on Kobane on September 16, hoping to quickly seize the small town and secure its grip on a large stretch of the Syrian-Turkish border, following advances it made in Iraq.
At one point, it looked set to overrun the town, but Kurdish Syrian fighters, backed by coalition air strikes and an influx of Iraqi Kurdish peshmerga forces, have held back the group.
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