Liverpool midfielder Fabregas has been ruled out of Tuesday's 2-1 win over Aston Villa with a hamstring injury.
The Brazil international, who was not allowed to rest for the match like Diego or Mohamed Salah, appeared to have suffered an ear injury within half an hour and cut the pace before half-time.
He has been replaced by Jordan Henderson, and his involvement in the FA Cup final against Chelsea on Saturday has been widely publicized.
The 28-year-old did not think his condition was serious, but Clap revealed after the match that further tests were needed to determine the severity of the injury.
"He did not feel too much muscle," said Klopp. "He is positive, but I'm not sure what I can do about it. let's see.
"You have to make decisions before you play the game. No one has a problem and you have to play someone."
Left-back Andy Robertson, who has been left out of the squad due to injury, admits the loss of Fabinho at the crucial point of the season could be a big blow.
Liverpool, who need the most points in their remaining two games against Southampton and Wolverhampton Wanderers, are still in contention for the Premier League title if they hope to overtake Manchester City at the top of the table.
Liverpool are also in contention for a place in the Champions League final against Real Madrid on May 28, and Clap will sweat for Fabinho's involvement until a medical is completed.