Moyes has thus far refused to discuss terms on a new contract despite the fact that his deal expires at the end of the current campaign, but Kenwright remains hopeful the Scot will stay.
"He's made a simple statement, give me to the end of the season," Kenwright told Sky Sports News.
"He knows in making that statement it's not the easiest one for the football club and he's acknowledged that to me. But he also knows the respect I have for him.
"So hopefully in seven weeks when the last match is played we can have the five minutes that David has alluded to for the last six months or so that will sort out a new contract, a new adventure, and keep David at the football club.
"If it doesn't, the man leaves with his head held high."
That leaves the Toffees facing the prospect of needing to appoint a new manager in the summer for the first time in over a decade but Kenwright readily admits no plans are afoot.
Asked if discussions with possible replacements had occurred, he said: "Does the phone ring? Yes. What is my response? My response is very simple - Everton Football Club has its manager."
It also has its owner despite the fact that Kenwright has been open about the fact that he is willing to accept offers for the club.
Asked about the future ownership of Everton, he added: "They (the fans) don't want another Bill Kenwright. They want someone who can take it forward.
"There will be someone out there. This week, yeah, some more have come forward. You've got to remember, everyone knows the football club is for sale."