Asiacell will be the first of Iraq's three mobile operators to carry out a listing, the first major offering since a U.S.-led invasion in 2003.
In the past year, Qtel has spent $2.16 billion to increase its holdings in Tunisiana and Kuwait's Wataniya to 90 percent or more, pointing to a strategy of tightening its hold over existing units rather than expanding its 17-country footprint across the Middle East, Africa and Asia.
Muddying this approach has been Asiacell, Iraq's No.2 telecommunications operator and 53.9 percent owned by Qtel, which must offer a quarter of its shares for public sale as part of its license obligations.
The sale process is opaque and it is unclear whether Asiacell's shareholders would be selling their shares on a proportional basis.
The idea of selling would be at odds with a $1.5 billion deal struck in June by the former Qatar monopoly to up its stake in Asiacell to 60 percent from 30 percent.
Market sources said they expected Qtel to use the share sale to acquire the outstanding shares it still needs to meet its target.
"According to the information I have, Qtel will not sell its shares, it is a buyer," Layth Sulaiman, head of the ISX board of governors, told Reuters.
Qtel could even raise its stake further, although that may depend on demand from other investors.
As of 1100 GMT, the Iraq Stock Exchange (ISX) had received orders for 46.92 billion Asiacell shares, it said in a statement, or 69.5 percent of the 67.5 billion shares on sale. These are priced at a minimum of 22 Iraqi dinars ($0.02) each.
If buy orders are less than 75 percent of shares offered, the sale will be cancelled and the process will start again.
But the bookrunner and bourse officials have said this was unlikely, with many investors preferring to subscribe in the final days so that their money is not tied up for long.
Brokers will be able to place orders for the shares until 0630 GMT on Sunday, with trading set to begin later that day.
The share sale is technically not an initial public offering because Asiacell has already carried out a nominal IPO to convert to a joint stock company as required under Iraqi law.
Asiacell and domestic rivals Zain Iraq, a subsidiary of Kuwait's Zain, and France Telecom affiliate Korek all missed an August 2011 deadline to float a quarter of their shares.
Demand from foreign investors for the Asiacell share sale exceeded that of Iraqis, Sulaiman said.
(Writing by Matt Smith in Dubai, Editing by Andrew Torchia and David Cowell)