Former defender could take charge of at the weekend after and his assistant, Sipke Hulshoff, were sent off on Wednesday night.
Slot in the aftermath of Everton's dramatic late equaliser against the Reds, who played out in the Merseyside derby.
Abdoulaye Doucoure and Curtis Jones by celebrating in front of the travelling Liverpool fans post-match.
And the red cards shown by Oliver will have repercussions for Liverpool at the weekend, with Slot and Hulshoff likely to be banned for Sunday's match with .
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That means Heitinga, who made 140 appearances for Everton and moved to Anfield in the summer to join Slot's coaching team, could lead the Reds at the weekend, as outlined by .
Slot's red card meant that the Liverpool chief was also unable to fulfil his post-match press duties or shed any light on the conversation he had with Oliver prior to his dismissal.
Speaking on TNT Sports, former Everton defender Phil Jagielka pinpointed why Slot may have been unhappy with James Tarkowski's 98th minute equaliser after a nudge in the penalty area in the build-up to the goal.
He said: "You can see why Arne Slot was furious. There was a slight little nudge in the box and if that was my team I would be appealing. I would be getting sent off after the game too.
"Slot always talks about staying composed but it seems like he lost a bit of his composure at the end there. That's what a derby does to you."
Slot was also unable to comment on the post-match brawl that saw Jones and Doucoure sent off, although .
"It was a very big provocation from one certain player," the Dutchman told Match of the Day. "I think Abdoulaye Doucoure wanted to provoke our fans, I think that is what I saw and Curtis Jones didn't think it was the right thing to do.
"We all saw it and reacted as a team as we were able to do. You know what happens nowadays, it becomes one big tussle. Then it is not me who has to deal with it, it is the referee and today I am not sure he had it fully under control."
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