Dyche's Burnley went on to record a shock 1-0 win at Anfield that day, ending Liverpool's 68-match unbeaten run at home.
The two managers clashed at half-time of the feisty affair, exchanging words in the Anfield tunnel.
Both Dyche and Klopp played down the spat which was caught on camera, while the now Everton manager later joking: "There was nothing in that.
"He felt my coat wasn't good like John McGinn did, and he mentioned it. And I say 'Well, you weren't the first to get there. John's already referenced my coat'. That one cleared that up.
"Look, I think fans don't mind that. They want to see two managers fight for their teams, for their clubs, standing up.
"After the game it's gone, for me it's done. That's it. End of."
Now speaking ahead of the Merseyside derby, Dyche has once again spoken about the incident and his relationship with Klopp, insisting there is no issue between them.
He said, via the Liverpool Echo: "Every manager should be passionate about what they do.
"That sort of thing gets blown up. That's the reality as I see out. There's not a manager I've fallen out with. I've never had a problem with Jurgen Klopp. There is nothing wrong with showing a bit of passion and commitment to the cause."
Dyche's Everton go into Saturday's game as big underdogs, having won just once at Anfield in the last 20 years. Dyche, meanwhile, has only beaten Klopp as a manager twice in 13 meetings.
The Toffees manager added: "Their record is very strong. Our record needs changing. It is a tough place. We will not be listening to the noise around it.
"We know they are a very good outfit and we know our record needs changing there. It is a tough place to go and it is a big game but our performances have generally been very strong recently. We want to come together and deliver another one."
Despite a reputation for physical football, Dyche also suggested Everton will need to keep things calm on Saturday in order to get a result.
He said: "The game is not as physical as it was when it comes to challenges. It's difficult to win games if you haven't got the right amount of players. Control and focus is important."