Just days before the two sides meet in the Champions League, the Bayern president said he and Klopp "agreed on a collaboration together" 11 years ago.
Liverpool are now taking a breather from their Premier League title challenge and, next week, will concentrate on the Champions League when they host Bayern Munich in their last-16 first leg at Anfield.
The match will see a renewal of acquaintances between the former Borussia Dortmund coach, who for several years saw his side lock horns with the mighty Bavarians for glory in Germany and in Europe, and his one-time nemesis.
Ahead ot Tuesday night's game on Merseyside, Bayern president Uli Hoeness spoke of how, 11 years ago, Klopp - then at Mainz - was deemed a top target to replace Ottmar Hitzfeld ago prior to the appointment of Jurgen Klinsmann.
In that case, Dortmund came up top over Bayern, as Klinsmann would only last one year before departing, while Klopp led his side - who had endured a lean period in the 2000s - to several trophies and also establishing foundations upon which future coaches have also impressed.
"Personally, I have a high opinion of Jurgen Klopp," Hoeness is quoted by Sky Sports News as saying. "Many years ago we agreed on a collaboration together, but we ended up signing Jurgen Klinsmann instead. There I showed I respect him and his work a lot. It's going to be a tough task for both sides. I hope we'll come out on top."
Could this be an example of Bayern trying to play mind games? Making seemingly benign comments in the press harking back to the past which could theoretically sow negative emotions in the Reds manager's head? Self-doubt, regret, or anything else that could knock him off complete focus?
Let's face it, it's been 11 years since this alleged 'near-miss', and Bayern have faced Klopp multiple times. Why is this story coming out now, just days before they face off? The Reds boss is surely savvy to this kind of thing and shrug it off, but he and his players definitely need to watch out for any more apparent mind games ahead of the first and second leg.