France, Egypt agree Rafale, military hardware deal - source

* Deal includes 24 Rafales, frigate, missiles for 5-6 bln eur

* Egypt deal would be first overseas sale of Rafale fighter jets

* Le Monde says deal to be signed Monday in Cairo (Adds French govt official, background)

PARIS, Feb 12 (Reuters) - France and Egypt have agreed a deal worth more than 5 billion euros ($5.7 billion) for the sale of Dassault Aviation (Paris: FR0000121725 - news) -built Rafale fighter jets, a naval frigate and missiles, a French source close to the matter said on Thursday.

The deal would make Egypt, which has been looking to upgrade its military hardware on fears the crisis in neighbouring Libya could spill over, the first export customer for the French warplane.

"Yes, there is an agreement," the source said in response to a report in Le Monde newspaper which said the two countries had initialled the deal on Thursday.

Le Monde said the final page outlining the modalities would be signed on Monday by Egyptian President Abdel Fattah al-Sisi and French officials, possibly President Francois Hollande or Defence Minister Jean-Yves Le Drian.

A French government official said the talks had not ended.

"The Egyptian president has not made his decision on the French offer," he said. "The discussions are not finished, the dialogue continues."

Egyptian government officials and Dassault executives could not immediately be reached for comment.

The deal includes 24 Rafale jets, a Fremm naval frigate and MBDA air-to-air missiles.

The contract with Egypt would be the first overseas for the Rafale 14 years after it entered service and three years after manufacturer Dassault Aviation entered exclusive negotiations to sell 126 of the combat jets to India.

Delays in finalising the Indian contract are expected to be discussed at a major Indian air show starting on Feb. 18.

Dassault, which is also in negotiations to sell the Rafale to Qatar, is under increasing pressure to sell the jet overseas.

The French government said last year it would slow the pace at which it takes delivery of Rafale jets, taking just 26 over the next five years instead of 11 a year. .

Paris and Cairo have enjoyed close economic ties in the past but turmoil in the north African state since President Hosni Mubarak was overthrown in 2011 left Western governments wary of signing contracts, especially in defence.

With the recent rise to power of Sisi, ties have improved. Both sides are concerned by the rise of jihadist groups in Libya and Egypt.

France secured its first major military contract in Egypt in about 20 years in 2014 with a 1 billion-euro ($1.35 billion) deal to sell four naval frigates.

The Fremm is built by state-controlled DCNS, which is 35 percent owned by French group Thales (LSE: 0IW5.L - news) . MBDA is a venture of Airbus Group (Swiss: AIR.SW - news) , Britain's BAE Systems (LSE: BA.L - news) and Finmeccanica (LSE: 0ONG.L - news) of Italy.

($1 = 0.8812 euros) (Reporting By Emmanuel Jarry, Marine Pennetier, John Irish, Cyril Altmeyerhenzien; in Paris and Yara Bayoumy in Cairo; editing by Andrew Callus and Ralph Boulton)