Despite Salah's incredible season, his campaign on a sour note when he was forced off with injury in Liverpool's Champions League final defeat to Real Madrid last month in Kiev.
Egypt's national team - including star striker Mohamed Salah - is gearing up for its first World Cup in 28 years, but matches are only being broadcast in the country by Qatar-based pay television network beIN.
"There's a good degree of progress but no definitive decision on whether he takes part, as we are following his case day by day", he told reporters.
Fans of the Pharaohs will be hoping their star man will be able to feature in all or most of Egypt's group games, as the man with 33 goals in 57 games for Egypt is by far their biggest threat and will provide the best chance to progress to the knockout phases.
Egyptians hoping to watch the World Cup for free have been offered a chink of light after the country's competition authority said it was obliging Federation Internationale de Football Association to let state TV show games.
Egypt are training at the Akhmat-Arena in Chechnya's capital Grozny.
Kadyrov, supported by Russia's President Vladimir Putin, rules Chechnya with an iron fist, drawing constant condemnation from human rights groups. Its group also includes Saudi Arabia and host Russian Federation.
Salah scored 32 times in the Premier League last season after the African forward moved to Liverpool FC in a £39m deal from Serie A giants AS Roma last summer.