The German manager told The Times (via ESPN.co.uk): "I told [Gerrard] 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, 36, is an academy coach at Anfield having rejoined the club in a non-playing capacity earlier this year following the end of his time at Los Angeles Galaxy, per the Guardian's Andy Hunter.
He will take charge of the under-18 Liverpool side at the start of the 2017-18 campaign, per Paul Joyce in The Times.
Gerrard is one of Liverpool's greatest-ever academy graduates. He won a UEFA Champions League, two FA Cups and three League Cups with the club during his 17-year senior career at the club.
The former England captain left briefly for LA Galaxy and Major League Soccer in 2015, but his return to Merseyside always seemed inevitable.
And now it seems he is being primed to take over.
Klopp added that "it's perfect that we can involve Steven" and described him as "fantastic."
There will be swathes of Liverpool fans who would love to see their inspirational former captain lead the side from the touchlines, and it is far from out of the question.
Klopp is doing a fine job at Anfield, and it does not seem likely he will vacate the top job any time soon.
But, when he does, Gerrard could well be one of the candidates to take over.