England midfielder Rice remains on the sidelines for now with a knee injury sustained on international duty last month.
But West Ham manager Moyes said: “Declan’s been training really well. It’s all gym based at the moment.
“He’s working really hard in the gym because he wants to get back as quick as he can.
“He’s obviously got other reasons, he knows he’s got the Euros coming up in the summer as well.
“As you can imagine for any club to lose Declan Rice would be a big blow, but at the moment we’ve been able to carry it and I hope we can continue to do so.”
West Ham visit Newcastle on Saturday with wins over Wolves and Leicester taking them back into the top four.
Victory on Tyneside would move them above Leicester, who are in FA Cup semi-final action on Sunday, and into third ahead of next weekend’s home game with fifth-placed Chelsea.