The process initially began in January but stalled in the summer as the economic crisis worsened.
An appointment is expected in December, with those invited to pitch thought to include WPP Group's combined media agency Group M along with Universal McCann, owned by Interpublic.
The pitch is being overseen by Orascom chairman Naguib Sawaris, the Egyptian billionaire who owns the majority of the company. Consultancy firm Booz & Co was hired to help manage the pitch process.
Orascom owns the mobile operator Wind Italy and Wind Greece, which is where the majority of the media budget is spent, and the focus of the first round of pitching.
Other markets to follow are Algeria, Pakistan and Bangladesh, with billings for the five markets expected to be worth more than $400m (£277m).