England players and staff have been advised not to use public Wi-Fi in Russia, including the connections provided at the team hotel.
According to media reports, the FA has also strengthened firewalls, introduced encrypted passwords and have strict guidelines for players regarding social media.
The FA could not immediately be reached for comment.
England, who lead Group F with 20 points, can seal their participation in the World Cup with a win over Slovenia in their penultimate qualifying match at Wembley on Oct. 5.
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Hacking group Fancy Bears in August leaked anti-doping information regarding footballers and said more than 150 players failed drug tests in 2015. Athletics governing body the IAAF said in April it had suffered a cyber attack that it believed compromised information about athletes' medical records.
The group has been linked by Western governments and security experts to a Russian spy agency blamed for some of the cyber operations during the 2016 U.S. election. Russia has denied meddling in the election.
"We can confirm the FA has sent a letter to FIFA related to the Fancy Bears attack. In its reply, FIFA has informed the FA that (it) remains committed to preventing security attacks in general," a FIFA spokesman was quoted as saying by British media.
"With respect to the Fancy Bears attack in particular, it is presently investigating the incident to ascertain whether FIFA's infrastructure was compromised," the spokesman added.
The spokesman was quoted as saying FIFA was relying on expert advice from third parties on computer security.
"It is for this reason that FIFA cannot and does not provide any computer security advice to third parties," the spokesman said.
(Reporting by Aditi Prakash in Bengaluru; Editing by Alison Williams)
