The deal is likely to include a firm order for 12 CS300 jets, and could be announced as early as Tuesday at the Dubai Air Show, according to the report.
Bombardier has faced a series of problems over the plane, most recently a trade dispute in the United States that imposed a 300% import tariff.
Earlier this month an unnamed European airline said it meant to buy at least 31 of the C-Series planes.
Bombardier Commercial Aircraft President Fred Cromer said the deal "confirms the need for right-sized aircraft in the Middle East".
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C-Series wings are made at Bombardier's Belfast operation, providing employment for about 1,000 people. The jet, the larger of two C Series versions, can carry 130 to 160 passengers. Swiss and Air Baltic Corp., which began flying the CS300 in December, have reported better-than-expected fuel efficiency, which is key to the jet's appeal.
The Airbus deal should make Bombardier programme "strong", Musallam says, but it does not appear to have swayed the carrier's decision.
The shopping spree, following months of negotiations, marks an expansion push for Egypt's flag carrier after it weathered slumping tourist visits and a fatal crash in 2018.