Arsenal currently lead at the top of the table by five points, with United an extra three points adrift in eighth position, but Moyes believes that the title race remains open despite the North London side's early advantage.
The 50-year-old told Sky Sports News: "I said at the start that Arsenal have got the same chance as all of the rest of us. It's an open Premier League.
"They've had a really good start at this present time, but you can only decide who's going to win it come the end of the season."
Moyes takes United to the Emirates Stadium to face Arsenal on Sunday afternoon.