The combined group would have 130,000 employees.
Luxottica and Essilor are planning a merger, Reuters reports.
The 45 billion euro (US $47.8 billion) deal was set to be announced on Monday prior to the opening of the market, according to the news agency, which cited "a source with knowledge of the matter."
The Financial Times also reported on the agreement, describing it as a 50 billion euro (US $53.1 billion) deal. According to the newspaper, which also cited unnamed sources, Luxottica founder Leonardo Del Vecchio "will become the largest single shareholder in the merged group and will control 31 per cent of voting rights."
Luxottica, based in Milan, Italy, is the largest eyewear firm in the world, with a brand portfolio that includes names such as Ray-Ban and Oakley. Its retail division includes many well-known names, including LensCrafters, Sunglasses Hut and Pearle Vision.
Essilor, which makes lenses as well as instruments and equipment, is based in France. Its brand portfolio includes names such as Varilux, Crizal, Transitions and Foster Grant.
Together the companies would have about 130,000 employees, according to the Financial Times.