Both players were substituted during the club's 3-2 defeat to Arsenal at the Emirates Stadium yesterday.
Diaz and Alexander-Arnold could be out of action for quite some time going by Klopp's comments.
He told Liverpoolfc.com the following: “Lucho we had to change before (half-time). (It's) something with the knee, not good.
“He will have a scan and then we will know more. I have no idea about the extent and then on top of that Trent is bad as well with the ankle.
“(He) twisted the ankle, not good. Trent never, in seven years, went off if he could have played on. He was in too much pain, it started swelling immediately, so we will have to see.”
Anfield Watch Verdict
Liverpool are having a horrendous season. The Reds have only secured two Premier League wins from a possible eight games.
Now, Klopp has lost two of his starters. The German isn't having much luck at the moment.
It would be fair to assume that Joe Gomez will come in for Alexander-Arnold. The Englishman replaced the Scouser against Arsenal yesterday.
So, the Reds should be able to cover Diaz for the time being. We will just have to wait and see how serious the aforementioned injuries are.
We wish Diaz and Alexander-Arnold all the best.