Firmino was forced off during the second half of Saturday’s 2-1 victory over Tottenham Hotspur after being accidentally poked in the eye by Jan Vertonghen.
Jürgen Klopp, the Liverpool manager, still hopes to be able to call upon the Brazilian for his side’s opening Group C game at Anfield.
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However, when asked whether Firmino would definitely be available to play on Tuesday, Klopp said: “No, not definitely. If we played today, no chance, but we all hope there is a chance for tomorrow.
"That is good news, that it will be close. When everyone saw the pictures after the game, we were all shocked.
"When we had first-hand contact with him, after he was in hospital, it was a big relief for all of us.
“It is painful and no-one needs that but he will be fine – we just don't know exactly when. Another 30 hours before the game? We will see how it develops.”
If Firmino fails to recover in time, Daniel Sturridge is likely to take his place in Liverpool's frontline and make the first Champions League start of his five-and-a-half-year spell with the club.
“He will be ready,” Klopp said of Sturridge, though the Liverpool manager finds himself down to the bare bones in attack after injuries to Dominic Solanke and Divock Origi.
“If Bobby can’t play, and Dom [Solanke] and Divock [Origi] can’t, then we are short of options. They got little injuries in the U23 game with Swansea. There is no problem with the first line-up.”
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