The JC has learnt of a married couple from Damascus living in Istanbul but trying to make aliyah.
The woman was born Jewish but converted to Islam for her Muslim husband. It is understood that they have not been welcomed by the local Turkish Jewish community.
Yigal Palmor, the Jewish Agency’s director of public affairs and communications, said there was a chance that the woman could be granted refuge in Israel, but not her husband.
He said: “The problem is the woman has converted to Islam.
"She is not qualified under the law of return to come to Israel as an oleh.
"The husband is Muslim. Obviously, because he is not married to a Jew, and not a Jew himself, he does not qualify."
He added: “She could get entry into Israel under another law, which would allow her to come on a temporary visa. Things could be arranged here one way or another.
“If she accepts coming here without her husband, that could be arranged relatively easily, including a possible reconversion.”
Mr Palmor also said that over the past five years, at least a dozen Syrian Jews have been rescued and granted refuge in Israel.