The Reds legend is consistently linked as a future replacement for Klopp, who is expected to leave Anfield when his contract expires in 2024.
But Gerrard is unhappy about the speculation as he is "very happy" in Glasgow.
Asked about the constant links to his old club and England, Gerrard told ESPN: "I can't control any media speculation about my position.
"I don't welcome it, I don't add to it. All I do is focus on the job I have here and I'm very flattered and grateful for the position.
"I'm very happy here, I've said it on numerous occasions, it's a huge club, I'm settled, I'm happy and I can continue to develop and keep trying to push this team forward."
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