Moyes said that Rice is recovering from the knee injury he suffered on international duty in March but would not confirm when the England midfielder will be available for selection.
“We're obviously getting closer to getting Declan back, because we're another week down the line and we're hoping that we can have him available," said Moyes, ahead of Sunday's meeting with Everton.
“He's back on the grass and closing in on it. Undoubtedly he's a big miss for us and we'll try to get him back as quickly as we can.
“He's so important for us and we need to get him back as soon as we can. He can make the difference in the games and we have a big game coming up this weekend for a starter.
“We've got a few people back on the grass, back training. We've got another day before we get to game time and we're hoping we can get them back, but I wouldn't put any timescales on it exactly for when I think it'll happen."