Asked about Klopp's prospects at Anfield, Hummels said his former manager would be a perfect fit.
"There's no doubt he's a fantastic coach and when people put their mind to the question of 'what does he do post-Dortmund?' then clubs like Liverpool naturally come into the equation," Hummels told reporters at a news conference in Dublin ahead of Germany's Euro 2016 qualifier against Ireland.
"He eats, lives, breathes and thinks football day after day and is a fantastic addition to any team. I'll keep my fingers crossed for him in his next venture," the 26-year-old defender added.
Klopp also received the backing of German national coach Joachim Loew.
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"I'm not really party to the negotiations but I do know talks are taking place," Loew said.
"He's had a fantastic, extraordinary time in Dortmund and created lots of emotions among the supporters.
"Looking from afar, there are comparisons you can make between Dortmund and Liverpool in terms of the supporter culture of both clubs. If they can work it out, he can be a great addition to any team."
(Reporting by Simon Jennings in Bengaluru; editing by Sudipto Ganguly)
