Goalkeeper Vito Mannone is a doubt for Sunderland's Premier League fixture at Southampton on Saturday after picking up an elbow injury.
Jordan Pickford is set to play in Wednesday's League Cup tie at home to Shrewsbury Town, but the absence of Mannone will come as a blow to the Black Cats, for whom striker Fabio Borini remains sidelined.
"Vito has a problem with his elbow that we're worried about and he will have it checked out," Moyes said at his pre-match news conference.
"I don't think Fabio will make it. There's not much change with the others: Sebastian [Larsson], [Jan] Kirchhoff and Lee Cattermole are long-term."
Moyes went on to stress that Lamine Kone - a reported target for Everton - would not be leaving the Stadium of Light, saying: "We expect Lamine to be back in for treatment tomorrow. He's still a Sunderland player and he will remain a Sunderland player.
"Steven Pienaar needs game time but at the moment it's a real balance because we really don't have much to juggle with.
"I always take the cups seriously. There will be one or two changes but there won't be many. The younger boys are already playing."
Moyes' side have lost their opening two Premier League games 2-1 and he is running out of time to add to his squad with the transfer window set to close on August 31, but the Scot still wants to bring in new players.
"I'd like to get a few in if we can," Moyes said. "There are only eight days to go and we're working very hard.
"We need to make improvements, get players in and there's a lot of work I need to do with the players."