"Andy's back in training. We got him back at the start of the week and we will keep monitoring him," Moyes told a news conference on Friday.
"He's trained for a few days, so we'll see how he is. He's obviously not played for eleven weeks, and I've got that in my mind as well... (but) he's champing at the bit."
Midfielder Manuel Lanzini (knee) and defender James Collins (hamstring) have also shaken off injuries and could be available for the final stretch of the season as Moyes targets an unbeaten run to secure their top-flight status.
West Ham are 14th in the league table with 34 points, six points above the relegation zone. The London club are edging towards safety having defeated Southampton 3-0 late last month and holding champions Chelsea to a 1-1 draw in their last game.
"If we can keep the form going. I don't see any reason why we shouldn't aim to go unbeaten until the end of the season. That should get us enough points to stay up," Moyes added.
"We want to get 10 wins... we've got eight. The magic number is 40 points. We don't have enough, but the performances we've put in the last two games have given everyone a real lift."
Stoke are second from bottom with 27 points.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Christian Radnedge)
