The Barcelona midfielder has joined Bayern on a season-long loan.
Coutinho told Bild: "[Klopp] sent me a message and wished me the best of luck.
"He wrote that Bayern is a big club, that the Bundesliga is a great league and that he is very happy to see me there."
Coutinho went on to detail how Klopp "breathed new life" into the Reds upon his arrival and said he was honoured to work with the former Borussia Dortmund coach.
"He's just a great coach, one of the best in the world," added Coutinho. "He is a real leader. I learned so much from him, especially on a mental level.
"He changed Liverpool. He breathed new life into the club, made it really strong again. It was an honor to work with him."