There was certainly no love lost between the two sides in the days of Jose Mourinho and Rafael Benitez, but it seems they've moved on a fair bit since then.
Antonio Conte and Jurgen Klopp seemed on good terms during Friday night's game, with the Reds boss obviously the happier of the two after his side escaped Stamford Bridge with a 2-1 victory.
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In fact, Conte even reacted graciously when his Liverpool counterpart forgot to shake his hand at the final whistle.
As is becoming the norm after a Liverpool win, Klopp delighted fans by going absolutely crazy at full time, hugging his players and generally celebrating as if his side had just beaten one of their main title rivals - which they probably had, if the season pans out as we expect.
In all that commotion, however, the eagle-eyed reporters at the Mirror spotted that Conte was left hanging as he waited for the usual post-match gesture.
Klopp goes crazy
Take a look at Klopp's epic celebrations here:
According to the same newspaper, Conte simply laughed and walked down the tunnel after realising the handshake was never going to come, even if it's the first thing managers normally do at the final whistle.
The German almost certainly won't have meant to offend the Chelsea manager with his snub, as it seems he was just getting carried away with the enormity of what his players had achieved.
Huge three points
The Blues were unbeaten going into the game, so this was yet another sign that Liverpool are going to be serious contenders this season.
Dejan Lovren and Jordan Henderson got the goals - Henderson's an early contender for Goal of the Season - matched only by a single Diego Costa reply. It was definitely Liverpool's night.
Who knows, Klopp may well have even rectified his mistake when he finally made it into the tunnel, but as a man who's known for some crazy celebrations himself, it's no wonder Conte wasn't too bothered.
Who do you think will finish higher - Chelsea or Liverpool? Let us know in the comments.
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