He said: "Kenny and Stevie have both been a really big support from day one. If Liverpool were to sack me tomorrow, then maybe Kenny would be the first choice to replace me, but they would probably bring Stevie down from Glasgow.
"If you ask who should follow me, I'd say Stevie. I help him whenever I can."
Reacting to the comments, Gerrard said: "I was surprised and flattered at the same time.
"But when you read the quote really carefully, like I have, it said 'if I get sacked tomorrow' he thinks Steven Gerrard should be the next Liverpool manager.
"Jurgen Klopp's not getting sacked tomorrow. I don't want him to get sacked tomorrow. He's doing a fantastic job.
"I'm a Liverpool fan. I'm sure every Liverpool fan on the planet endorses what I'm saying here. We want him to stay for many, many years and bring as much success to our club as possible.
"But yeah, it was very flattering at the same time."
Both Klopp and Gerrard are under contract at their respective clubs until the summer of 2022.