Speaking after arriving in Kuala Lumpur on their pre-season tour, manager Andre Villas-Boas told the club's website: "At this moment he is having a medical but has not yet agreed personal terms."
The 19-year-old was first choice for Genk last season, making 40 appearances in the Pro League, and also received his first call-up to the senior Belgium squad.
"Chelsea see me as the successor to Petr Cech. It won't happen in one or two years, but in three, four or five years," said 6ft 6in Curtois.
"We received an enormous offer that gave us no choice but to let him go," said Genk director Dirk Degraen.
Genk added that Chelsea's offer was "by far the largest bid" they had ever received for any of their players.