Goodison boss Ronald Koeman has had his eye on the 20-year-old since he was in charge at Southampton and Gray was still at Birmingham.
The winger has been used sparingly since his move from St. Andrews, which has alerted the Dutchman to a potential January bargain.
Everton will be hoping Gray can fill the void left by Bolasie following the £29 million signing’s rupturing of his anterior cruciate ligament.