The incoming French diplomat, Gerard Araud, also said the Jewish state was "paranoid", the Israeli newspaper Yediot Aharonot reported on Sunday.
One of the daily's correspondents, Boaz Bissmuth, said he had been eavesdropping on a conversation between Araud, who is due to take up his post in September, and two other veteran diplomats in the gardens of the Quai D'Orsay.
The correspondent said he then introduced himself to the incoming ambassador, who told him, "You don't intend to write that," explaining that his comments were made in the course of a private party.
However, the correspondent wrote that he believed that the comments "were sufficiently serious" to warrant their publication.
Israeli Education Minister, Limor Livnant, told Israel's public radio that Israel should not sign the diplomat's letter of accredition if he had used words ascribed to him.
"But we must verify what he said," the minister added.
The French charge d'affaires in Tel Aviv, Michel Miraillet, said that "we do not have any comment on this matter."