Delegates have been split over the two candidates, with Hosni, a veteran Egyptian government minister, being dogged by allegations of anti-semitism.
Hosni, who has been Egypt's culture minister for the past 22-years, caused concern among some observers after he was quoted as saying he would burn Hebrew-language books.
He has also been associated with media censorship in his home country and sparked anger among Muslim groups there when he said the hijab was a "step backward" for Egyptian women.
Bokova joined Bulgaria's foreign ministry UN and disarmament department in 1976, becoming the country's foreign minister for a brief period in 1996-1997.
'Man of peace'
She has witnessed Bulgaria's transformation from Eastern Bloc nation to European Union member.
Someone from the Arab world or Eastern Europe has never run Unesco.
Supporters of Hosni say the Egyptian's election would send a positive signal from the West to the Muslim world, but the race has been clouded by charges that anti-Israel comments made last year make him unfit for the role.
Hosni's detractors include Auschwitz death camp survivor and Nobel laureate Elie Wiesel, who says his appointment would "shame" the global community.
But he is also behind efforts to rebuild a crumbling old synagogue in Cairo, Egypt's capital.
At the Unesco headquarters in Paris, supporters hailed Hosni as "a man of peace" who would improve ties with Muslim countries.
Hosni has long been front-runner in the race for the post but the charges have clouded his candidacy.
|If selected, Irina Bokova, pictured, would be the first woman to head Unesco [AFP]
Unesco's executive council started voting last Thursday for a successor to Japan's Koichiro Matsuura as director-general.
Hitting back at charges of anti-Semitism, Hosni has insisted his comments were part of an angry exchange in parliament with hardliners from the Muslim Brotherhood and were taken out of context.
The Egyptian minister is seeking to become the first representative from the Arab world to head the UN agency which is mandated to promote global understanding through culture, education and science.
The appointment is to be endorsed in October by the 193-member assembly of Unesco.