Following Egypt's exit from this summer's World Cup in Russia, it emerged that Salah was considering ending his international career with the Pharoahs as a result of disagreements with the EFA.
Issues such as image rights and the controversial handling of a meeting with Chechen leader Ramzan Kadryov are believed to be among the reasons for the 26-year-old's discontent.
However, EFA executive manager Tharwat Sweilem has dismissed the idea that there is a problem between the two parties, insisting that the Reds talisman remains Egypt's key player in the pursuit of future success.
"I would like to congratulate Mo Salah for his new contract at Liverpool, I wish him all the best. He is an Egyptian and Arab phenomenon who makes us feel proud," Sweilem told Goal.
"He’s the star of Egypt and our hope for the next stages, and there’s no problem with him."
Crowds of Egypt fans descended upon Salah's home in the wake of reports suggesting that he was close to ending his international career and he responded by coming out to meet them.
The Liverpool attacker subsequently posted a message on Twitter which suggested that his time as an Egypt player was not over, while also stressing that "there needs to be change".
Salah played in just two of his country's games at the World Cup in Russia, with a shoulder injury that he picked up in the Champions League final earlier in May curtailing his involvement.
Salah scored his second World Cup goal by firing Egypt ahead in the final group game against Saudi Arabia, but his efforts were in vain as Salman Al Faraj and Salem Al Dawsari scored to secure a Saudi victory.
Egypt finished bottom of Group A and coach Hector Cuper stood down from his position following the poor performance.
The EFA are now on the lookout for a new head coach to lead them into the next period and Sweilem has emphasised that any prospective candidate must share their ambition as they look to qualify for the 2022 World Cup.
"We are trying to sign with a new coach who meets our needs and ambitions," he said.
"The new coach is expected to stay as the head coach of Egypt national team until Qatar 2022."