In what is to be Baghdad’s largest stock listing, the move is part of Qtel’s strategy to focus on gaining control of its international units.
Qtel recently spent $2.16 billion to increase its holdings in Tunisiana, and Kuwait's Wataniya to 90%.
Asiacell has been offering a quarter of its shares to the public, as part of its licencing obligations, which has complicated Qtel’s aim of increasing its stake.
Some details of the share offer have not been disclosed, according to Reuters, and it is unclear whether all shareholders are putting their shares up for sale.
Despite some confusion, sources maintain that Qtel is in the market to increase its stake in Asiacell and not decrease it.
An initial deal worth $1.5 billion was struck in June last year to raise its stake to 60%, but 6.1% of the stake is still pending regulatory approval, with Qtel considering an IPO to achieve that level.
Reports suggest international demand for the Asiacell offer has exceeded demand from domestic Iraqi companies.
