The Football Association is reviewing an incident where a Newcastle staff member appeared to throw an object towards the Liverpool technical area during the Reds’ 2-1 win on Wednesday.
Players and staff from both teams clashed after Fabio Carvalho’s 98th-minute winner at Anfield.
It is unclear if the incident, captured on television, sparked the melee in front of the dugouts.
Newcastle declined to comment when contacted by BBC Sport.
The FA will also consider other factors in the build up to the confrontation.
Boss Eddie Howe called the late winner a “sickener” after his side had led 1-0 through a debut goal from £60m record signing Alexander Isak.
Roberto Firmino equalized for Liverpool before Carvalho hooked in from close range to win the game with almost the last kick.
Referee Andre Marriner had added on five additional minutes, but several Newcastle players went down with cramp, while goalkeeper Nick Pope also suffered an injury during the extra time.
When asked about Newcastle’s apparent time-wasting, Klopp said of Carvalho’s goal on BT Sport: “It’s the perfect response to that. I am really happy about that.”
The German added: “I don’t know when the kicking the ball away stopped being a yellow card. When did this rule die?”