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Rosenberg, 31, is a civil aviation pilot who enlisted in an Israeli army search-and-rescue unit before being arrested in 2009, extradited to the United States and jailed over an international phone scam, one of her former lawyers said.
'They [the Kurds] are our brothers. They are good people.' —Gill Rosenberg, Canadian-Israeli fighting with Kurds against ISIS
On Monday, Israel Radio aired an interview with Rosenberg in which she said she had travelled to Iraq, was training with Kurdish guerrillas and would go into combat in next-door Syria.
The station did not name the interviewee, who spoke North American-accented Hebrew, but a source involved in the report identified her as Rosenberg.
"They [the Kurds] are our brothers. They are good people. They love life, a lot like us, really," Rosenberg said, explaining why she joined up after contacting the guerrillas over the Internet.
A source in the Kurdistan region with knowledge of the issue said Rosenberg was the first foreign woman to join YPG, the Kurds' dominant fighting force in northern Syria. She has crossed into Syria and is one of around 10 Westerners recruited by YPG, the source said.
Rosenberg could not be reached by Reuters for comment. A source provided an Iraqi Kurdistan cellphone number for her, but it was turned off on Tuesday.
A Facebook page registered to Rosenberg showed photographs of her in settings marked as Kurdish areas of Iraq and Syria.
"In the IDF [Israeli army], we say 'aharai', After Me. Let's show ISIS what that means," read a Nov. 9 post.
Yahel Ben-Oved, an Israeli lawyer who represented Rosenberg in the U.S. criminal proceedings, said she had no knowledge of her joining the Kurds though they had spoken recently. "It is exactly the sort of thing she would do, though," said Ben-Oved.
Rosenberg had consented to extradition and served around four years in a U.S. prison under a plea bargain, according to court documents.
A 2009 FBI statement on the case names her as Gillian Rosenberg, among 11 people arrested in Israel "in a phoney 'lottery prize' scheme that targeted victims, mostly elderly."
Israel's NRG news site reported at the time that Rosenberg turned to crime after running short on money, that she was estranged from her parents and had tried in vain to join the Mossad spy service.
Israel has maintained discreet military, intelligence and business ties with the Kurds since the 1960s, seeing in the minority ethnic group a buffer against shared Arab adversaries.
The Kurds are spread through Syria, Turkey, Iran and Iraq. In the latter country, they have the autonomous Kurdish Regional Government (KRG).
Israel bans its citizens from travelling to enemy states, among them Syria and Iraq. It has been cracking down on Israeli Arabs who return after volunteering to fight with Islamic State or other rebels against Syrian President Bashar al-Assad's rule.
Canada similarly worries about its citizens fighting in Syria. Israeli and Canadian officials said they were aware of Rosenberg's case.