The Brazil international suffered an eye injury in the Reds' 2-1 win over Tottenham Hotspur at the weekend, forcing him to sit out training on Monday.
Speaking before that final session at Melwood ahead of the Group C clash with PSG, Klopp revealed at his pre-match press conference that a late decision will be made over Firmino's availability.
"If we played today, no chance, but we hope there's a chance for tomorrow," he said. "It's good news that it will be close for the game because we were all shocked from the pictures.
"We had contact with him in hospital and was a big relief. It was painful, but he will be fine, we only don't know exactly when. We will see how it develops."
Liverpool are also expected to be without Dominic Solanke and Divock Origi, who both picked up minor knocks in an Under-23s game at the weekend, leaving Xherdan Shaqiri and Daniel Sturridge as the only other back-up options for Firmino.