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The former Reds captain, 36, is to return to his former club as a youth coach in February in what will be his first job since retiring as a player.
Klopp said he "had a good long chat" with the ex-England skipper, describing his appointment as "wonderful news".
"He said he wants to be a manager in the future. That's cool," Klopp added.
"It was important to know what Steven wants. Being a manager is a job you have to learn and he is ready to make steps.
"Combining his playing experience with all the things he has to learn, he has a bright future. Everyone in this room knows better than I do he is a wonderful guy and it's wonderful news for football."
Gerrard made his Liverpool debut in 1998 and left Anfield at the end of the 2014-15 season to join MLS side LA Galaxy having won the Champions League, Uefa Cup, FA Cup and League Cup on three occasions.
He retired as a player in November after a 19-year career.
Gerrard had been linked with the manager's job at League One side MK Dons after announcing he would leave LA Galaxy, but said the opportunity came "too soon" for him.
He is also working towards his Uefa A coaching licence, which is required to manage in the Premier League.
Liverpool boss Jurgen Klopp says he will do "everything I can" to help Steven Gerrard develop into "the best manager he can be".