Moyes took over from Slaven Bilic in November 2017 on a six-month deal leading to speculation that West Ham will seek a different longer-term replacement.
The club have categorically refuted these claims, backed up by Moyes who hinted that his future may remain in London.
He told reporters: "I've always said that I will wait until the end of the season.
"We have to make sure we are still a Premier League team. I'm not going to have any discussions before then. I get on with the chairman and we speak regularly but we are both more than happy to wait until the end of the season.
"I've had inklings, yeah. But I'm going to wait until right until the end of the season and make my decision then. I'm enjoying it because there is a lot of confidence around the camp now. The players believe we can be a Premier League team next season so let us get that part of the job done and we'll get onto the other stuff later."
West Ham take on Arsenal at the Emirates on Sunday.