The 37-year-old swapped clubs in 2014 after five seasons at the Santiago Bernabeu, where he won six major trophies.
Alonso left Madrid three months after helping them to Champions League glory and went on to spend three years with Bayern before announcing his playing retirement.
Explaining his reasons for wanting to leave the Spanish giants, Alonso told The Athletic: "I was so curious to find out [Guardiola's] secrets.
"He has a relentless natural enthusiasm. Football seasons are long but right until the very end, Pep never seemed to be tired.
"He was alert, always ready. For the players, maybe this gave us an extra few metres in our legs when it mattered most."
The former Spain international, who played against Klopp's Borussia Dortmund side during his time at Madrid and Bayern, said: "I didn't enjoy playing against them because they made it so intense, you'd almost break.
"It was like he wanted you to be in a cage. He wanted to trap you. There was an organised pressure. I was under pressure all the time.
"I enjoyed the mood around those games because they were so important but the challenge of beating Dortmund was immense."