Mainz fans slam Klopp's Red Bull move with banner in Leipzig game
Using a play on words with Klopp's last name, the home fans asked "Are you crazy?" and used a quote from their side's former boss: "I like people until the point they disappoint me."
A larger banner, in big red letters, asked Klopp if he had "forgotten everything we gave you?".
A former player at the club, Klopp coached Mainz for seven years, taking the team to the top flight for the first time before moving to Borussia Dortmund and later Liverpool.
Klopp stepped down as Liverpool manager in the summer having won several titles, including the Premier League and Champions League.
In October, Klopp announced he would join energy drink company Red Bull, which owns clubs in Leipzig, Salzburg and New York, as their global head of football from January 2025.
His decision to take up the job at Red Bull has annoyed supporters in Germany - particularly at ex-clubs Dortmund and Mainz - who have a long-standing dislike of RB Leipzig.
Some fans believe Leipzig, founded in 2009, are not consistent with Germany's 50+1 rule, which requires member control of clubs, while others have hit out at the multi-club ownership model used by Red Bull.
Leipzig's win at Mainz sent the club, who are yet to lose in the league this season, top of the table - at least until Bayern Munich's match against Stuttgart at home later on Saturday.
Leipzig coach Marco Rose, who played under Klopp for several years at Mainz, dismissed the fans' criticism as a minority opinion.
"There are 35,000 people in the stadium, many of whom have an opinion. I believe that around 34,936 people love Kloppo for the fact that he shaped an era here, that we achieved something great together," said Rose.
"He was here in Mainz for a long time.
"Everyone has their own life somewhere and the right to decide things freely and for themselves. Not everyone has to love it."
Rose added that: "(He) didn't even notice (the banner), so it can't have been that wild."