Qatar's move marks the first time an Arab state has requested Israel's help in obtaining one of the 10 rotating seats on the 15-member security council, and comes amid increasingly warm relations between the two countries.
"Qatar has asked the Israeli government to support its candidacy for the UN Security Council," Israeli Foreign Ministry spokeswoman Amria Oron told the Al-Arabiya news channel on Tuesday.
"Evidently we will look into this request on the basis of the positive relations between Qatar and ourselves and we hope to give a reply in the course of the coming days.
"We think that relations with Qatar are very important given that it is the only Arab country in the Gulf to have relations with Israel," she said, expressing hope that relations "will expand further in the next days or months".
When asked about the request by Aljazeera, Qatar's ambassador to the UN, Nasir bin Abd al-Aziz Nasir said: "We asked all members of the UN, including Israel, for their support and we received a positive reaction."
Qatar has played host to an Israeli commercial mission since 1996, and visits by Israeli officials to Doha have become a relatively frequent occurrence.
Qatari Foreign Minister Hamad bin Jassem bin Jabr Al Thani met his then Israeli counterpart Shimon Peres in July 2002 in Paris, at a time when other Arab countries were freezing their contacts with Israel.