The Toffees' chairman admits that the manager has a decision to make, stating that he had "served the club wonderfully well", but confirmed he would be in charge against West Ham
The Scot will replace his compatriot at Old Trafford, with the Toffees lining up a move for Wigan boss Roberto Martinez.
Moyes, who is out of contract this summer, met Kenwright in London on Wednesday. However, while the 67-year-old says he is unaware of any deal between United and Moyes, he concedes that the decision is Moyes' to make.
"I don't know about a deal being done. David had a meeting scheduled with me and we had a good meeting," Kenwright told Sky Sports News. "I think at the end of the day, David's contract is up in six weeks' time and he has a right to make his own decisions. He's served this club wonderfully well and he has a right to make his own decision.
"It's 22:45 BST and you've been waiting for me all day, I really just want to go home now, see the dogs, have a cup of tea and go to bed. I don't know anything about [reports of Moyes leaving]."
Kenwright also confirmed that Moyes would be in charge of the Toffees' Premier League game against West Ham this weekend.