The footage was leaked onto X - formerly known as Twitter - on Monday and allegedly shows Coote with an unknown male at some point during a coronavirus-enforced lockdown.
The unknown friend asks the man purported to be Coote about a Liverpool game in which he was the fourth official, to which he answers "Liverpool were s***" before he was asked what he made of Klopp.
The man alleged to be Coote replies "c***" before also labelling the German "f****** arrogant" and claiming that he has no time for people like him, referring to an incident where Klopp had "a right pop" at him in a match against Burnley.
"He accused me of lying, and then just had a right f****** pop at me," Coote purportedly says. "I've got no interest in speaking to somebody who's f****** arrogant, so I do my best not to speak to him."
Coote goes on to speak positively about James Milner, before allegedly insulting Klopp once again by saying "German c***, f*** me", and the man beside him finishes by making disparaging remarks about people from Liverpool.
A second, shorter video then shows the man alleged to be Coote saying: "Just to be clear, that f****** last video can't go anywhere, seriously," while the other male replies: "He's a Premier League referee, let's not f****** ruin his career."
PGMOL confirm Coote suspension after alleged Klopp X-rated rant
The Daily Mail reports that the PGMOL are looking into the footage, and the governing body have not ruled out the possibility that the video is not genuine, either being deepfake or AI generated.
Now, the PGMOL have confirmed in a statement that Coote has been immediately suspended pending a full investigation, and they will not make any further comment until they have completed the process.
"David Coote has been suspended with immediate effect pending a full investigation. PGMOL will be making no further comment until that process is complete," the statement read.
Coote was the referee for Liverpool's 2-0 victory over Aston Villa on Saturday evening, which took Arne Slot's side five points clear of Manchester City at the top of the Premier League table.
Liverpool are yet to publicly comment on the matter.