Liverpool can tighten their grip on a top-four spot on Sunday (23 April), having collected six points from tricky away games against Stoke City and West Brom in recent weeks. Klopp's options have dwindled since the victory at the Hawthorns last Sunday, however, with Dejan Lovren his only centre-half to train on Thursday.
Speaking at a press conference on Thursday broadcast on Facebook Live, Klopp explained: "There are a few little things from last game which doesn't make it easier. There is a little muscle problem with Joel Matip, a little thing with Lucas Leiva. There is still a problem with Klavan, there was a very, very small medial ligament [problem], very small, but it could mean there is not enough time for Palace."
Facing a shortage of options at the back, Klopp could turn to Joe Gomez to fill the void. After returning from a long-term knee injury last year, the former Charlton Athletic starlet has largely been limited to games for the club's Under-23 ranks, but did feature in three FA Cup fixtures in January.
After another positive performance against Leicester City's Under-23s on Monday, Klopp says the 19-year-old could be an option.
"We have to find a solution for the weekend, today I don't have to find one for next year. It's not 100% Lucas can't play, it's not 100% Joel can't play, it's not 100% Ragnar can't play, but they are not in training at the moment. So that is not too cool. Joe Gomez did well on Monday, for the Under-23s, and made big steps in the last few weeks so maybe now we have to try this pair [Gomez and Lovren]. We will see, I don't know in this moment."
Adam Lallana, meanwhile, returned to first-team training this week having missed the club's last four games. He suffered a thigh injury suffered during a routine 2018 World Cup qualifying victory over Lithuania in March.
"Unfortunately things are not too positive," Klopp said of Liverpool's injury situation. "Adam in a good way, yes, he's back on the pitch but still with the rehab coach so nothing changed, we are not sure exactly when he will be in normal training next week, Wednesday, Thursday maybe."
There is still no timeline on Jordan Henderson's return from a foot injury though, with the captain now facing the possibility of not playing again this season.
On Henderson, Klopp admitted he does not know when the midfielder will return. "At this moment he cannot really train so we have to wait for this moment. If there was something else to say I would say it but there isn't. We are in talks with different medical departments but we have to wait."
Liverpool also remain without Sadio Mane, who will not play again this season having undergone knee surgery. Elsewhere, Klopp dismissed any injury concerns over Roberto Firmino following reports the Brazil international has been training away from the group this week. The Reds boss also had good news on Danny Ings, who his "running again" after the serious knee injury suffered last November.