The Hammers were without Mark Noble, Tomas Soucek and Ryan Fredericks for the midweek Premier League win over Norwich City at the London Stadium.
Long-term absentee Angelo Ogbonna is still sidelined while Said Benrahma is away at the African Cup of Nations with Algeria.
Moyes is preparing his team for a second clash against the Whites in seven days following last weekend's FA Cup meeting.
Leeds were beaten 2-0 in the capital in England's oldest cup competition though they now travel south again for a top flight clash.
The Scot, though, refused to be drawn on who may or may not be available to face Marcelo Bielsa's outfit.
"I don't want to be specific on who has Covid and who is injured but those two [Soucek and Noble] were out and we are hoping we might get one of them back, but I am not saying who," Moyes told his pre-match press conference.
"We might get one of them back and we also have some niggles, which we picked up from the game [against Norwich].
"We've also got some other players who have had Covid as well. So we're trying to work around it like every other club at the moment. It's difficult but we've got injuries and Covid like all clubs have."
Defender Kurt Zouma - who has been out since early December with a hamstring issue - has returned to training in recent days and is battling to be fit.
"Kurt Zouma is on his way back and doing quite well in training, he has just started back really," Moyes added.
"He is another player who unfortunately has gone down with the virus [Covid] but those things are the same at all the clubs, whether it be injuries of COVID but we have to deal with it and move on and do the best we can."