Hummels and Klopp won back-to-back Bundesliga titles in 2011 and 2012, adding the DFB Cup to what became a domestic double in the latter season.
Klopp is now enjoying success on Merseyside, although that comes as no surprise to Hummels, who admitted the Bundesliga leaders were glad to avoid the Reds in the draw for the quarter-finals of the UEFA Champions League.
Watch: Klopp's emotional Dortmund farewell
"I know how strong Klopp’s teams are," said Hummels, who played in the 2013 Champions League final that Dortmund lost to Bayern, to England's Daily Mail. "I know how good his teams are when they get to this level.
"His teams always perform at the highest when they face the best teams. That's for certain. I don't think there was a team remaining who wanted to face Liverpool. They work so hard, they play so intense and aggressively with the quality of players they have — especially up front."
Communication between the pair has remained open despite their respective departures from Dortmund, where he says they enjoyed a special relationship.
"It was almost like family between us," said Hummels. "Of course we had our issues from time to time. One day we would be there, screaming at each other. But the next day? It was all fine. He understood me, I understood him.
"Each of us would know why the other one would act like he did. We never, ever had a big problem. He always considers what you say. He doesn’t always agree and he has the final word. But he considers it and he will say 'OK' or… 'Think about it again.' He is the boss."
Hummels' boss now is Heynckes, at least until the end of the current season, which is when the 72-year-old's contract expires and he is expected to return to retirement, leaving behind a void that will be hard to fill - and one Klopp himself has been linked with.
"[Heynckes] sees the things when they are not working out on the pitch," Hummels said. "He talks about it afterwards and tries to change it. You can see why he has been successful. He is quieter than Klopp but not as quiet as you may think. He is not loud but he is direct.
"You can say it loud, you can say it quietly… what matters is that the things you say make sense. We have to be at our peak. It feels like we have been there, from time to time, but not for weeks and months."
Watch: Heynckes' Bayern fine-tuning
With the Bundesliga title as good as wrapped up, hitting that peak in the business end of the season in terms of the cup competitions is the aim for Hummels, who is keen to be on the winning team in Kiev this May: "[I want] the biggest trophy in club football. It's the hardest competition there is. We want to win it."
Bayern will look to take a step closer to that objective when they travel to Sevilla this Tuesday for the first leg of their quarter-final clash, with the return leg at the Allianz Arena a week later. Liverpool face Manchester City in the last eight before, who knows, Klopp and Heynckes could be in opposite dugouts in the semi-final, or perhaps even in Kiev.