After an incredible turnaround under Moyes, the Toffees moved 17 points clear of the relegation zone with nine games remaining and have lost just once in their last 10 Premier League fixtures. Following former boss Sean Dyche's departure not many would have predicted such a change in form but Moyes does not believe he can celebrate just yet.
The club will move into their new 52,888-seater venue next season, which fans have already attended alongside current Everton players. Moyes, however, spoke to talkSPORT about how he will not be visiting before Premier League football is confirmed for next season.
"I've not been to the new stadium yet because I'm not going to go until I feel as if we are safe. It looks a lot easier, the league table, than when I first came in. It's a much better feeling than what I had when I arrived.
"But I have to say, we look as if we're in a good position. It will be tough for a lot of teams below us to catch us. But we hope to try and keep winning and get ourselves into an even stronger position."
"If we were going to be a Championship team, I don't know if it'd have been me who'd still be doing that job," Moyes said.
"I want to make sure that when we go, we're a guaranteed Premier League team. It's looking like that at the moment, but football can change.
"I'm not counting my chickens yet."
Everton are fifth in the Premier League's form table since Moyes took over and unless the side completely fall apart they are on course to survive this season as the likes of Southampton, Ipswich Town and Leicester City go back down to the Championship.