Kop legend Gerrard has returned to the club and will take charge of the Under-18s this summer.
Former Dortmund boss Klopp signed a six-year contract extension at Liverpool last July and has no plans to depart any time soon.
But the German, in an interview with The Times, has said he hopes that Gerrard will eventually succeed him as manager.
Klopp said: “I told him when I leave, or the club sack me, I don’t care of course who’ll be my successor, but I’d love that he’d be it.”
Gerrard returned to the club having called time on his playing career, following an 18-month sojourn in the United States with LA Galaxy.
The 36-year-old joined the academy in February with a roving coaching role but will assume full-time responsibility for the Under-18s, when Neil Critchley steps up to the Under-23s.
“It’s perfect that we can involve Steven,” said Klopp. “What a guy, he’s fantastic.
“I’ll do everything I can to make sure he gets all the information he needs. Because when you join a club, you have a big responsibility for the future, and the future of this club needs legends like Steven Gerrard in decisive positions.”
Klopp’s deal ties him to the Merseysiders until 2022.
The Reds will qualify for the Champions League with victory over Middlesbrough on Sunday.