Both sides, Klopp's present and his past respectively, are currently top of the league, with Liverpool and Dortmund both six points clear at their own summits.
While Dortmund have lost once, Liverpool have yet to taste defeat in the Premier League and are in pole position to win their first title of the Premier League era.
Klopp, though, remains wary, insisting that while Dortmund only have to deal with Bayern Munich, while the Reds are facing challenges from Manchester City, Spurs and Arsenal, among a number of others, including Chelsea and Manchester United.
“It's true that in recent weeks we have often sent congratulatory text messages back and forth [between Dortmund and Liverpool]," he told Bild.
Klopp says that the title race is far from over, too, despite Liverpool taking a commanding lead after Manchester City fell to two successive defeats, falling behind Spurs to third.
“We should all look at the calendar: the only thing that's over is the first half of the season," he added.
"It's undeniable that we've played exceptionally so far, but we're only half way. I don't waste thoughts on anything else.”
While Klopp claims Dortmund only have to deal with Bayern, he too will have to find a way to beat the Bavarian giants as the Reds prepare to take on the German champions, who are currently second in the Bundesliga, in the Champions League.
“It's going to be tough games for both teams," he added.
"What happened [to Bayern] this season doesn't matter, we have to prepare ourselves for the best of Bavaria. We've seen in the past two or three weeks before the winter break that they're strong again.”