Former England international Gerrard is in his first season working in Liverpool's academy after choosing to start his coaching career at his boyhood club.
However, media speculation has linked the 37-year-old with Scottish club Rangers, who have Graeme Murty in charge until the end of the season following the departure of Pedro Caixinha last October.
"He was, is and forever will be a Liverpool legend. But whatever he wants to do, we will support him," Klopp told the media ahead of Liverpool's Premier League fixture with Stoke City.
"I don't even know what the situation is at the moment – no one has told me any decision.
"Clubs are interested in signing Stevie. He had a massive amount of experience as a player - I think I would talk to him as well if I owned a club.
"One day it will happen, either here or somewhere else. But it’s his decision. We will support him in all directions."
Klopp also revealed his disappointment at not getting the chance to work with Gerrard during his playing career - and jokingly warned the Liverpool legend to forget about calling him if he takes charge of a rival club.
"The relationship is brilliant. I'd have loved to work with him as a player, but was a little late for that," the German added.
"But from the first moment we have developed brilliantly. As a Liverpool coach in the youth system, you have a good bunch of players to work with - you don't have to necessarily tell them everything about football.
"If he thinks he's ready, he's ready. That's a big if, but we will be happy and support him.