Express Sport understands Gerrard has held talks with Rangers about potentially succeeding caretaker boss Graeme Murty at Ibrox.
And the former Liverpool captain would take a wealth of experience to Glasgow with him following a stellar playing career.
Gerrard has been back at Anfield in a coaching capacity since last year and is currently in charge of their Under 18s side.
Klopp has offered his backing to Gerrard with a possible move to Rangers on the cards at the end of the season.
“I’m not worried,” said Jurgen Klopp on Friday morning.
“Steven was, and is, a legend. Whatever he wants to do.
“Nobody told me anything about it, any decision.
“I can imagine clubs are interested in signing Stevie.
“I would think about him as well if I owned a club!”
Klopp also previewed Saturday’s showdown with Stoke at Anfield.
“It will be a real challenge,” he added.
“I know Paul [Lambert], he’s a [Borussia] Dortmund legend.
“They are very intense and direct, a lot of fights for second balls.
“I was in that situation many times – fighting to stay in the league.”
