The arms contract could be officially signed on Wednesday or Thursday, Le Monde reported without saying where it obtained the information.
Officials from Egypt's army and the presidency could not immediately be reached for comment. A French government official also declined comment.
Dassault Aviation, which builds the Rafale, declined to comment. This would be the first export deal for the fighter jet.
Laurent Collet-Billon, the head of France's DGA defence procurement agency, said on Monday that he was "relatively optimistic" of securing a deal to sell arms to Egypt including Rafales.
The Fremm frigate is built by state-controlled DCNS, which is 35 percent owned by defence electronics group Thales . MBDA is a joint venture of Airbus Group, BAE Systems and Finmeccanica. ($1 = 0.8864 euros)
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© Thomson Reuters 2015. Reporting by Alexandre Boksenbaum-Granier in Paris and Shadi Bushra in Cairo. http://af.reuters.com/article/egyptNews/idAFL5N0VK2R320150210