If someone wants to figure out problems at Liverpool then surely he needs to check all things related to this club as there is no doubt Mane having good impact on Liverpool performance in last few years, and he was key player for them with few injuries are also having big impact as Firmino and van Dijk both are also not available which is also having negative impact on their performance.
Klopp has been frustrated by how many teams have pushed him to the breaking point and turned him into a laughing stock after selling Mane, who was a part of their greatest achievement, and despite the new players they have brought in, there hasn't been any improvement in their play. However, I anticipate that they will ask Firmino and Van Dijk to return for Champions League games, unless they want Salah and Gakpo to suffer their losses at the hands of Real Madrid.
Right now, Klopp is doing his best for changing fortune, but things are not working in his favour but good thing happening Liverpool management is giving him good time which is positive as he still capable of changing things in team's favour even this season is going to be nightmare for them, but hopefully they will have positive change at the end.
If Liverpool doesn't hire a new manager, Klopp will obviously make a wholesale switch on players like Firmino and those who are always injured. He has three years more left at the club on his contract, which is more than enough time to improve the club.