Moyes, 49, has spent 11 years at Goodison Park but his current contract is up at the end of the campaign, with speculation intensifying about his future.
The Scot has been widely applauded for keeping Everton consistently challenging in the top half of the Premier League on a limited budget.
English media reports have linked Moyes with a close-season switch to Chelsea.
"I've spoken with the chairman (Bill Kenwright) and I want to see how the team do," Moyes told reporters.
"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."
Everton, who face third tier Oldham Athletic in the FA Cup fifth round on Saturday, are sixth in the Premier League having lost only four games all season.
They have a number of injury concerns after their league defeat to Manchester United on Sunday.
Striker Nikica Jelavic, however, is pushing for a recall after finding himself on the bench in recent weeks.
"I don't know what it does for anybody but you hope that they sit back and look at exactly what they have to do to get back into the team and get their real form back," Moyes said. "It's part of football.
"Hopefully when he gets his opportunity he will be ready to take it. Maybe a little bit of a rest at times can help."