When asked about a possible move away from Merseyside, Moyes commented: "No. That is not my plan and it is not in my thoughts.
"I will have a chat with the chairman [Bill Kenwright] at the end of the season and we will see where things go. It will just be a chat generally to see where we are."
Moyes celebrated 10 years in charge of the Toffees this year after he took over from Walter Smith in March of 2002.