Koscielny suffered a muscular injury during the Gunners' 2-1 loss at the hands of Watford on Saturday (14 October) while Ramsey and Sanchez missed the clash with thigh and hamstring injuries, respectively.
Arsenal's win streak was ended by the Hornets, who came from behind to inflict the defeat, and Arsene Wenger will be keen for his team to get back to winning ways when they visit Goodison Park on Sunday (22 October).
The French defender has been struggling with an Achilles injury since last season and it requires daily management, but his latest injury was suspected to be calf related. While the latter two on the injury list returned with knocks following their commitments with their respective national teams. But the manager is also likely to have considered their mental states after both Ramsey and Sanchez suffered disappointing losses that saw Wales and Chile miss out on qualifying for the World Cup next summer.
According to the London Standard, the trio will not be risked by the manager for Arsenal's Europa League clash against Red Star Belgrade on Thursday (19 October), but all are expected to return to training ahead of their visit Merseyside to take on Ronald Koeman's side.
Wenger will continue his philosophy of fielding a mixture of youth and experience when they travel to Belgrade for the Europa League with Jack Wilshere and Theo Walcott expected to return to the starting lineup. Olivier Giroud could also start, while Francis Coquelin could be given his first run out in over a month following his return from injury.
Among the youth team players, the likes of Reiss Nelson, Joe Willock and Ainsley Maitland-Niles could all be part of the matchday squad.