Koscielny was substituted inside the final ten minutes of Saturday's 2-1 defeat at Watford amid fears he had exacerbated a longstanding Achilles injury.
The centre-back requires daily management of the condition to prevent inflammation and had been a doubt in the build-up but it is understood he merely suffered cramp at Vicarage Road.
Koscielny is not expected to travel to Serbia for Thursday's Europa League match against Red Star Belgrade in a bid to ensure full fitness for Everton, a plan which is likely to apply to Sanchez and Ramsey.
The pair were left out officially due to fatigue from their exertions on international duty with manager Arsene Wenger also aware of the mental impact of Sanchez's Chile and Ramsey's Wales missing out on World Cup qualification in agonising fashion.
However, Wenger claimed after the game that Sanchez had a thigh problem while Ramsey was struggling with a tight hamstring but Arsenal are confident both players will be available at Goodison Park.
The Gunners will continue their policy of fielding a mixture of fringe players and youngsters in the Europa League with Jack Wilshere and Theo Walcott in line to start alongside youngsters Reiss Nelson and Ainsley Maitland-Niles.