The club's leading goalscorer suffered a serious hamstring injury in the warm-up in defeat against Manchester United.
Edwards said: Potentially, his hamstring is worse. We were in a position where he was feeling good and we were pushing, he was pushing as well, and he felt it again, so we've got to be really careful now. There's not long left of the season now is there, so I don't want to say that yet, but he's going to be longer, he's not going to be back after the (international) break."
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He added: "At the moment we're scoring goals, that is one silver lining to that, but we want out best players available and available for selection. Eli doesn't just help us from an attacking point of view, he helps us defend set-pieces, sets that press.
"You know how important he's been for us so it's a big player that's missing."