Russian hacking group Fancy Bear has been spotted targeting hotels across Europe to spy on high-profile and wealthy guests.
Reports claim the FA would provide its own internet access for players and staff, who would also be instructed not to use social media that could reveal tactical information or details of their location.
The FA wrote to FIFA to explain its concerns regarding cybersecurity after its own correspondence with the international association was leaked by Fancy Bear.
It also warned the association regarding the activities of the group, and is understood to be considering what the best options are for securing the England team's communications if they get to Russia.
FIFA has said that it is relying on third-party support for its own computer security and as such does not itself pass on advice to others.
Hackers linked with Russia's military intelligence agency - although Moscow denies they are affiliated - have allegedly targeted sporting associations in operations intended to discredit critics of Russia's involvement in athletics doping.
The group, known colloquially as Fancy Bear - or in the more academic language of security research reports as Advanced Persistent Threat 28 - was previously investigated by the FA after it stole and released information on anti-doping in football.
Sky News has contacted a spokesperson at the Russian Embassy for comment.