The Brazil international has been on the move again this summer some 18 months after leaving Anfield.
Back in the winter transfer window of 2018, the 27-year-old playmaker completed a big-money move to Barcelona.
A dream switch to Camp Nou quickly became a nightmare for the South American, as he struggled to produce his best while operating in the sizeable shadow of Lionel Messi.
Bayern have offered him a fresh start, in an agreement which includes a €120 million (£110m/$133m) purchase option, and Klopp is backing a proven performer to flourish in his native Germany.
The Liverpool coach told Kicker: “Coutinho didn't get to play in his preferred No.10 role all that much when he was with us, but he's a great No.8 and is a fantastic left winger because he's incredibly good in tight spaces and has the pace to exploit bigger spaces.
"He dominates football matches, and is a real asset if he can put his stamp on the team.
"Bayern needed him, and Bayern wanted him. If they can integrate him and get the very best out of him, the Bundesliga will have a top player on its hands."
He will now get the chance to prove himself in the position he considers to be his best, while donning an iconic jersey.
Klopp is expecting big things, with it his opinion that Coutinho shares many qualities with a World Cup winner who once excelled in the 10 shirt for Serie A giants Juve.
He added: "Coutinho has an unbelievable eye for goal from range.
"I haven't seen a player coming in off the left and striking the ball with such regularity and precision from those kind of positions since Del Piero."
Coutinho will be looking to make an immediate impact with Bayern and deliver on his big billing, with it possible that a debut outing could be made on Saturday during a trip to Schalke for the Bundesliga champions.