The Liverpool star damaged ligaments in his shoulder during the first half of their 3-1 defeat by Real Madrid in the Champions League final on May 26 following a challenge by Real captain Sergio Ramos.
"Salah is feeling great, he has recovered quickly… I can assure you I am almost 100 percent certain that he will play for us tomorrow, of course, if nothing unexpected happens," Cuper told journalists.
Meanwhile, a Sputnik correspondent reported Thursday that Salah trained with the rest of the national team's squad ahead of their first match.
Egypt will kick off their World Cup campaign against two-time champions Uruguay in Yekaterinburg on Friday.