The clubs' bitterness was at an all time high in the noughties with Rafa Benitez's Liverpool triumphing during Mourinho's time in charge at Stamford Bridge in Europe.
Liverpool knocked the Blues out of the 2005 Champions League semi-final thanks to Luis Garcia's famous 'ghost goal' and went on to beat AC Milan in the final to lift the trophy for the fifth time.
Mourinho's Chelsea were also unable to beat Liverpool in two group stage games that ended goalless in the 2005/06 campaign, before falling to them again in the semi-finals in 2007.
Former Chelsea captain John Terry, who won five Premier League titles in west London, admitted Mourinho's frustration at losing to Liverpool.
Speaking to former Reds defender Jamie Carragher in 2020, he told Sky Sports: "I remember the team talk Mourinho gave before we played after we won the league [in 2005].
"I think we were something like 20 or 30 points in front and he's going, 'there's no way you can lose this game against these'.
"He couldn't even say the name Liverpool, he couldn't even pronounce the team. He was like, 'you do not lose to these today, we're so much better than these'. That still kind of sticks there.
"It was a frustration because you always found a way to really settle the game in the away fixtures, in the big Champions League fixtures as well.
"But the home games were like, for us going into [Anfield], the atmosphere was probably the best I've experienced over the years as a player."
Terry believes Mourinho took a more cautious approach against Liverpool because he respected their players.
He added: "Frustration was probably the word, we won leagues and stuff like that, so I think we felt we were the better side, we just couldn't break you down a lot of the time, and got knocked out on a couple of occasions," he continued as Carragher listened.
"I think he respected the players you had, yourself, Stevie [Gerrard], I think at times he did change but mentally from us he was like, 'be patient, throughout the 90 minutes or the two legs we will come through the better team or the stronger team, so we don't have to go out there and win it from the outset'.
"In those games he definitely showed you a little bit more respect. I think that's a credit to Liverpool and the team you had.
"Even in the league I felt you were a lot better than what you achieved on a consistent basis year in year out.
"Him and Rafa had that rivalry, they hated each other really, because we came up against Liverpool so often and him, it was that rivalry. He didn't do it because of Rafa, I think it was out of respect because of the team you had.'"
Now the two teams are among the best in the country and will be vying for league glory this year. Current Chelsea boss Thomas Tuchel takes his Champions League winners to Anfield, which is live and exclusive on talkSPORT at 17:30 on 28 August.