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.
At a press conference before Saturday's FA Cup fifth-round tie against 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. 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, which is 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 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 games so far this season, the Toffees are sixth in the Premier League table.
He 'wants to see how the team do'. Ergo he has received an offer from another club, or is hinting that he's looking for one. Either way, he's off unless Everton finish 3rd or 4th- levi