West Ham will be without Felipe Anderson for at least a month after the Brazilian midfielder suffered a back injury against Sheffield United.
The Hammers are facing a packed schedule over the coming weeks, with West Brom in the FA Cup following Wednesday's visit to Leicester as well as Liverpool, Brighton and Manchester City to come before February's winter break.
Moyes is already without right-back Ryan Fredericks who suffered a hamstring injury during the Scotsman's second game in charge, as well as Lukasz Fabianski who was forced off against Sheffield United.
There has at least been one boost with the return of Michail Antonio to training this week and the forward is closing in on a return.
"Felipe has a problem with his back and it could keep him out for a while, four weeks we think," said Moyes. "Antonio is getting close.
"We could do with getting some back because of the busy programme but sometimes, game after game isn't bad as the players can focus on their form."
West Ham have already brought Darren Randolph back to the club this month to cover in goal and, while they are not close to securing any deals, the Hammers manager is keen to bring in at least another new face this month with midfield the priority.
"Probably the same story," Moyes said of their transfer business. "Trying to bring them in, trying to do it quickly if the right ones are there but you're hearing it from all the managers, it's not easy to do business in January.
"We could really do with players who hit the ground running but also for the future as well and trying to get that balance is not easy this month."