The German's contract expires in June 2024 but speculation on when he'll leave Anfield increased following Steven Gerrard's appointment as Aston Villa boss.
Many view Gerrard as the natural successor to Klopp but the former Liverpool star wants the current boss to stay for as long as possible.
At his pre-match press conference on Thursday, Gerrard told talkSPORT: "You'll never hear me saying it [the Villa job] is a stepping stone.
"I'm really honoured and proud to be in this position, I'm all in and will give this job everything it needs for it to be a success. I'll be 100 per cent committed and so are my staff.
"In football I don't think there's anything wrong in having dreams and aspirations but Liverpool have got a world-class coach that they're very happy with.
"If he was to sign a lifetime deal right now I'd be very happy for them and him."
Klopp didn't commit to Liverpool for the rest of his life but assured fans he'd still be at the club for a while yet.
He said: "I don't have to think about those kind of things, thank God, because we are in the middle of this season and that's all that we are focused on.
"I know managers often get asked about things that will happen in two-and-a-half, three or four years but I don't know. I haven't thought about it until you asked me about it and I don't want to.
"It's all fine how it is. It's over when it's over and it's far away from being so let's focus on that."
Klopp also confirmed that he's been in touch with Gerrard since he got the Villa job but refused to say what was said between the two.
He added: "There are messages but they are private… I'm looking forward to meeting him, that's true, I'm really happy for him.
"But what we write to each other, it's completely fine if that stays private."