A shoulder injury kept Salah out of Egypt's opening game against Group A favourites Uruguay, in which the team from north Africa were beaten 1-0.
Russian made a dream start, beating Saudi Arabia 5-0 to rise to the top of the group above Uruguay on goal difference and Egypt must at least draw with the host nation in St Petersburg on Tuesday to keep their World Cup hopes alive.
"Salah is fit," Cuper told reporters on Monday. "We always carry out a last physical test before we announce our line-up and today we will have an important test for him to see how he does.
"I think he will be able to play. He is an essential piece in our team."
Salah spent last season scything through some of the best defences in Europe, scoring 44 goals in all competitions for Liverpool in the most prolific campaign of his career.
He has scored 33 goals in 57 appearances for Egypt and was their top scorer in World Cup qualifying, sealing their place in Russia with a stoppage-time penalty against Congo that sparked wild celebrations in the soccer-mad country.
"He's a great player, a crucial player, that much is perfectly clear," the Argentine added.
"Salah is one of the best players in the world. For me there's no shadow of a doubt there. It's an honour and a privilege to coach him.
"On top of being talented, he is humble. He is a team player and that at least for me is extremely important now. He's an important player for us. Nobody can deny that. I say it with all due respect to the other players in the Egyptian squad.... I think he'll be able to play."
Russia coach Stanislav Cherchesov told reporters he had devised a tactical plan to keep Salah quiet and Cuper is delighted.
"I think it's great if their coach is only focusing on Salah," he said. "Whether Salah can be stopped or not, different coaches will have different strategies.
"Salah is a player who has enormous skill and I have to say when we don't have him, we feel his absence."
(Reporting by Simon Jennings, editing by Ed Osmond)
