Matip was forced to come off at half-time during the win at Spurs and he is due to undergo a scan on Friday afternoon.
Liverpool will know more about his injury then, but he is a doubt for Sunday’s trip to West Ham.
“Last night I was after the game, especially with that [Matip injury], pretty emotional just because at half-time the boys [are] sitting there,” said Klopp.
“Now, meanwhile, there are still glimpses of hope that it’s not serious. No, we don’t have the final result because the scan didn’t happen yet. So we know more in three or four hours hopefully.
“Fabinho has no chance for the weekend.”
Liverpool’s injuries leave them short at centre-back for their match with the Hammers. Captain Jordan Henderson is likely to have to fill in there again, while Nathaniel Phillips will hope to get another rare start.
The Reds have been linked with signing a new centre-back this month and Klopp has admitted that is possible.
“Look, I don’t know. But we will try,” said Klopp. “It is funny when you all think: ‘Oh Liverpool will be just fine with the situation and they don’t care or try.’
“We try but there is nothing to say until something happens. We will see. The situation yesterday didn’t make it easier but we still try to do the right things. If that’s possible, we will do it. If not, we won’t.
“My thoughts didn’t change [after Matip went off against Tottenham], but my words might have. That’s probably my English.
“Same situation as before. We work always on this. That’s what we did all the time. We will see.”