The England stopper is currently on loan with Serie A side Torino, but they are unlikely to have the funds to make the deal permanent in the summer.
But speaking at his pre-Crystal Palace press conference on Thursday, Klopp insisted he would not be prompting a push to sign Hart.
“We always think about the squad, we always think about the goalkeepers,” he told reporters.
“Is it about Joe Hart? We usually don’t talk about things like this but in this situation we can.
“He’s a fantastic goalkeeper, the goalkeeper of the English national team, highest quality.
“But we have the highest quality goalkeepers. That’s how it is.
“Not for us, not in the moment and hopefully not in the future, and that’s not because of Joe!
“We have two strong goalkeepers, and [Danny] Wardy’s at Huddersfield playing a great season. Bring him back next year and there is competition!
“We have the young ones, they make big steps, really big steps, Caoimhin [Kelleher] and Kamil [Grabara], that’s really good.
“The situation around our goalkeepers is really good. I cannot give the answer a few people want, but we think about it all the time.”