The Toffees have made an offer of £250,000 for the 17-year old striker but Killie boss Kenny Shiels suggests he should remain at Rugby Park to continue his development.
"The boy's head has been pickled with talk of Everton," he told the Daily Record.
"There are negotiations taking place at the top end of each club.
"I have spoken to Matty's father and told him what I think is the best thing for his son's career. A young lad's career is the most important thing here, not finances."