Former Qatari culture minister Hamad bin Abdoulaziz Al-Kawari is now leading the contest, with French ex-culture minister Audrey Azoulay and Egyptian rights activist Moushira Khattab locked in joint second.
China on Friday said it will continue working for the development of the United Nations Scientific and Cultural Organisations (UNESCO), a day after the USA announced it was pulling out of the Paris-based agency.
Khattab has secured 12 votes in the second round of election, which was held Tuesday at the UNESCO headquarters in Paris.
The head of UNESCO is selected by a vote of its executive board members and Qian got five votes in the third round of voting, while Egypt's Moushira Khattab got 13 votes, the Post report said.
Arab states believe the job of director-general of the 195-member organisation should go to one of them for the first time, but regional tensions have complicated the task.
The campaign to succeed UNESCO's outgoing chief Irina Bokova was overshadowed by Washington's announcement Thursday that it planned to withdraw from the body after years of tensions over decisions seen as critical of Israel.
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Former Qatari culture minister Hamad bin Abdulaziz Al-Kawari is now leading the contest, but he has been unable to pick up support from other Gulf states who are part of a Saudi-led coalition blockading the gas-rich monarchy.
UNESCO has been accused of bias in the Israeli-Palestinian conflict, and it infuriated Israel and staunch ally the United States by granting full membership to Palestine in 2011.
On Wednesday, a prominent American Jewish organization charged that the Qatari frontrunner has sponsored "projects and programs with blatant anti-Semitic content."
Arab countries have complained that UNESCO has never had a boss from their region.
However, UNESCO does not observe the kind of rotation by world region which is used when choosing a UN secretary general.