Egypt are on Great Britain's red list, so Salah would be required to quarantine upon his return from Cairo and miss two Premier League games.
Egypt are scheduled to play Angola in Cairo on Sept. 2 before traveling to face Gabon three days later in Franceville.
The association said they "continue its contacts with the FIFA .... to have international players be exempted from travel restrictions imposed on them in countries where they play due to coronavirus.''
The Egyptian federation also wanted Salah to play for the national team at the Tokyo Olympics, but said Liverpool denied the request.
Clubs are not obligated to release players for the men's Olympic tournament.
Salah, who has twice won the Premier League's Golden Boot award, tested positive for the virus during a visit to Cairo in November, where he attended his brother's wedding.
At the time, he was to join the national team for its game against Togo.
The 29-year-old Salah was the first Egyptian player to become a Premier League champion after joining Liverpool in 2018 from AS Roma.
Liverpool are seeking to strike a new deal to keep Salah with the club.