Moyes, who has been in charge for the past 11 years, is out of contract in the summer but does not intend to make a decision on a new deal until the end of the season.
He said: "Being at Everton is something I would be really happy with.
"But we have been talking for a long time now, three or four months and everyone nudges along a little bit further every time we speak. As I have said, we will conclude that at the end of the season.
"What I am trying to do is make sure I give Everton the best chance of going forward. I wouldn't want it any other way.
"I would never do anything, in any way, to jeopardise Everton or the football club. I want to make sure the supporters see a promising, fresh-looking team for the seasons to come. We have to make sure the finances we have give us the opportunity to do that.
"We have a small squad, and in truth we have an ageing squad as well, which we need to look at. I need to be capable of being able to make those changes for the best of Everton.
"We are well aware of where we are at this moment in time. I have always said that where we finish, what we do at the end of the season - that will be a better time for us to make a decision than just now."
When asked about Kenwright's revelation that he has already received calls about the manager's job, Moyes said: "It is a great job, Everton. It really is."