The 49-year-old's current contract at Goodison Park expires at the end of the season and speculation is intensifying about his long-term future.
Ahead of Saturday's FA Cup fifth-round tie with Oldham, Moyes admitted he had spoken with Toffees chairman Bill Kenwright but he has no plans to decide anything until the current campaign is over.
"I've spoken with the chairman and I want to see how the team do," he said.
"I want to see how we do in the cups and the league and it is more than likely that I won't make a decision until the end of the season.
"You can ask me every week but I will probably give you the same answer."
Next month marks the 11th anniversary of Moyes leaving Preston to begin his reign at Everton, with his tenure regarded as a success despite him not having won a trophy during his time with the club.
The Toffees are enjoying a good season, and are in contention to qualify for the UEFA Champions League for the second time under Moyes' management after their debut in the competition in 2005/06.
Having only lost four games and taking 42 points from 26 matches so far this season, the Toffees are sixth in the Premier League table.
Everton goalkeeper Tim Howard earlier stressed the importance of Moyes staying with the club, but he insists that it should not be the concern of the players.
"The manager he needs to stay, everyone knows that," he told Sky Sports.
"It is no secret but that is an outside issue and that doesn't concern, currently, the players.
"We have to focus on the task and that is playing and performing, and he focusses on getting us ready for the games and performing and it [his future] is not something he talks about and we just get on with it."