West Ham currently have Victor Moses, Dimitri Payet, Manuel Lanzini, Diafra Sakho and Enner Valencia all out with injury.
The Hammers are without a number of key stars and their squad is being stretched to the limit at the moment.
To make matters worse, Victor Moses was forced to come off with a hamstring problem during West Ham’s most recent fixture against Manchester United.
But Bilic is optimistic that some of his players could make their way off the treatment table in the near future.
He is quoted as saying: "It's still too early [to tell with Moses], but it doesn't look good again. It's a hamstring - he felt it and we had to take him off.
"It's a big blow for us, but we have to stay positive as some of the players maybe have a chance of being back for the Stoke game. If not Stoke, then Swansea."
If Moses is ruled out for a considerable period of time, it will seriously weaken West Ham’s attacking options.
Dimitri Payet, Manuel Lanzini, Diafra Sakho and Enner Valencia are all currently nursing injury problems, leaving Bilic’s options short.
The Hammers’ form has been affected by their injury crisis, as they have now failed to win any of their last five matches.
West Ham are currently in sixth place in the Premier League table, having made an impressive start to the season. Next up for the Irons in the top flight is a clash against high-flying Stoke City, which certainly won't be easy.