"We have had talks with Everton and the player," Peter Ridsdale told the Echo.
"He should be with us for the start of pre-season training next week."
Dennehy, 19, is a tall centre half who can also play midfield. He is an Ireland U19 international and has been a regular in the Everton reserve team.
He will add competition to Roger Johnson, Glenn Loovens and Darren Purse.