Given Klopp is leaving the Anfield club in the summer, Alonso was touted as a replacement.
However, he has chosen to reject both the Reds and Bayern Munich to remain at Bayer for now.
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Klopp told a press conference on Friday: "A young manager being at a club that is doing really well, I was in a similar situation (at Mainz), I did pretty much the same.
I never regretted it. That's pretty much everything I can say about Xabi.
"He's doing an incredible job there. Leverkusen has a good team and will probably keep their team together (in the summer transfer window).
That's possible. It's not in all years like that. I understand that he wants to do that. For the other stuff, I have nothing to say about it to be honest."