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The Egyptian Football Federation said on Friday that Salah, 28, returned a positive test but is not displaying any symptoms.
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They added that the other members of the team had tested negative.
Egypt host Togo in Africa Cup of Nations qualifying on Saturday, followed by the reverse fixture in Togo on Tuesday.
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Salah will now self-isolate and could miss Liverpool's next two matches.
The Reds host Leicester in the Premier League on Sunday, 22 November, followed by a Champions League tie against Atalanta at Anfield on Wednesday, 25 November.
Salah has started all eight of Liverpool's Premier League games this season, scoring eight goals.
Egypt has recorded 6,417 coronavirus deaths since the start of the outbreak, and is currently recording around 200 new cases a day.
In September, Egypt allowed weddings to be held in open-air-venues after months of banning them in an attempt to stop the spread of coronavirus.
The government announced that these would be capped at a maximum of 300 invitees - with these only being able to take place in tourist and hotel facilities that obtained health and safety certificates.
Egypt currently sit third in Group G with two points from two matches. Comoros top the group with four points.
Liverpool are not due to play again until their home Premier League match against Leicester, which has been moved to a 7.15pm kick-off on Sunday, November 22.
The Egyptian has been in stunning form in front of goal for Liverpool this season, and is the joint-leading scorer in the Premier League with eight strikes so far.
Salah's news comes a day after it was confirmed Reds defender Joe Gomez had undergone knee surgery following an injury suffered in England training.
Liverpool said he had damaged a tendon in his left knee but there was no ligament damage.
Virgil Van Dijk has suffered a long-term knee injury while Fabinho is also sidelined.
England full back Trent Alexander-Arnold is set to be out for around four weeks after injuring his calf in Liverpool's draw with Manchester City last Sunday.