Reports emerged at the weekend suggesting that the Bundesliga champions are plotting a move for the ex-Borussia Dortmund chief, despite only signing a fresh long-term deal in July.
Klopp has made a hugely impressive start to his first full campaign on Merseyside, guiding the Reds up to second place in the Premier League - one point off current leaders Chelsea - and into the quarter-finals of the EFL Cup.
In the wake of speculation linking the German back to his homeland, Souness has told Liverpool supporters that they have nothing to worry about at this stage.
"I think he's fully bought into what Liverpool are all about," he told Sky Sports News. "I genuinely believe Liverpool are quite a unique football club.
"Once you work for them, it's with you for the rest of your life through the glory days of winning everything on a regular basis to the tragedies that have fallen onto the club as well.
"I think you quickly get Liverpool and I wouldn't think anytime soon Jurgen Klopp would be leaving Liverpool. I think he's fully bought into what Liverpool FC are all about."
Klopp's Liverpool side take on Leeds United at Anfield on Tuesday evening with a place in the last four of the EFL Cup up for grabs.