Mourinho has made the headlines with a number of feisty encounters with the media in recent weeks and most recently, he defended his managerial record and asked why Liverpool boss Klopp had not been questioned on his own failure to deliver silverware.
Klopp was unaware of the discussion, but he had no problem with the point Mourinho made and queried whether Mourinho's blockbuster briefings would be worth his time.
"What did [Mourinho] say? Now I'm interested," Klopp said after Liverpool's 2-1 win at Leicester City, before the conversation was explained. "He's right, that's right if he is speaking about me.
"There are probably a few more managers in the league but you thought it was about me, no problem. He is right absolutely.
"He is probably the most successful manager in the Premier League in that moment. I have no problem with that.
"I don't watch Jose Mourinho press conferences. Should I? I will start doing that. I cannot say anything about that. [I have] no clue what you are talking about to be 100 per cent honest. If he said I didn't win anything outside Germany then he's right, that's easy to see."
Meanwhile, as Klopp celebrated Liverpool's fourth win of the season at Leicester, home boss Claude Puel was left feeling frustrated.
"We finished the game with disappointment and frustration," Puel said.
"It is a good feeling, perhaps, because we have had the chances, we have had the possibility to take a point and perhaps, without conceding the second goal before half-time, to win the game.
"We played a good team, of course. They put us under pressure in the first half. We lost a lot of ball, we recovered some balls well. We lacked the good pass, the good tempo. That was a shame."