The Toffees are keen to bolster their wide options in January, with Charlton's Ademola Lookman looking set to sign and Manchester United's Memphis Depay also linked.
France Football reports that Pepe is another name under consideration. However, it is claimed the 21-year-old, who is also said to have attracted interest from Newcastle United (L'Equipe), is currently the subject of a €6 million (£5.1 million) bid from Lyon.
Reported Everton target Pepe (right) challenges Thiago Silva
Pepe shone for Orleans in last season's National League and has so far taken well to France's top flight, scoring twice and providing one assist in five starts.
One potential drawback, however, is a likely call up to Ivory Coast's squad for the upcoming African Cup of Nations tournament.
The France-born starlet won his first cap for the Elephants in October and has been included in Michel Dussuyer's provisional 35-man squad.
Charlton Athletic's Lookman (left) appears bound for Goodison Park
With Lookman and at least one other wide addition likely in January, Everton would perhaps be willing to wait for Pepe, although Lyon's approach could prompt the Toffees into action.
Goodison Park director of football Steve Walsh helped to discover a number of French-based talents for former club Leicester City.
Do Everton need Pepe?