Moyes, whose current contract expires at the end of the season, is yet to agree a new deal with the club, but both chairman and manager are confident an agreement will be reached when the time is right.
"We talk to each other three or four times a day," Kenwright told Sky Sports News. "He is a great manager.
"He and I both know we will be sitting down and talking about it."
Moyes earlier told reporters: "I've been here over 10 years, I've always worked hard and will continue to do so.
"I've got a great relationship with the chairman - I speak to him every day - and when the time is right we'll sit down and see where we're going to go."