Both firms on Wednesday announced a non-binding deal proposal, valuing Vodafone Egypt at $4.4 billion.
Once finalised, the regulator would have to approve it, the body said in a statement.
With 44 million subscribers and a 40% market share, Vodafone Egypt is the country's biggest mobile operator. The remaining 45% stake is held by majority state-owned Telecom Egypt.
(Reporting by Ehab Farouk and Ulf Laessing; editing by David Evans)