The Toffees have reportedly tabled a £250,000 bid for the 17-year-old, who has impressed in his two SPL appearances this season.
Kilmarnock manager Kenny Shiels confirmed that talks were taking place.
Shiels also insisted that he wants to keep Kennedy at Rugby Park and criticised Everton for unsettling him.
"The boy's head has been pickled with the talk of Everton," Shiels 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 best. A young lad's career is the most important thing here, not finances."
Everton assistant manager Steve Round confirmed yesterday that the Merseyside club are still looking to bring in players.
Everton face Leyton Orient tonight in the League Cup second round.