Hodgson was the oldest manager in the top flight by some distance, having come out of retirement to return to Palace last season.
Asked about ex-Reds boss Hodgson, Klopp told reporters: I think I said a couple of times I don't really understand why he is still doing the job! With my situation he'll probably understand a bit better, but I don't understand what he is doing!
One of the greatest I ever met, definitely, for that long time in the business (he is a) human full of experience. (He) trend-set in the beginning; he kept his idea. It's always like this when it's not going well.
That's the problem in our business then people forget a little bit how good the times were before. I think Crystal Palace could be like that if there were some supporters who were shouting for him to get the sack. They definitely forgot how good a job he did in the few times when he was there.
I hope he is doing well. I hope because that obviously was a shock last week when I heard about that he was taken ill in training. That's nothing that should happen at all. I hope he is doing well and when he is doing well then I wish him just the very best of times that he can have and stay healthy.
That would be the most important but it's a bit of a shame that I couldn't say properly goodbye to him because we faced each other quite frequently and like each other a lot. But, yeah, that's not the biggest problem."