In addition, sporting director Jorg Schmadtke will also leave his post at the culmination of the January transfer window.
The Liverpool boss announced that he is to stand down after eight-and-a-half-years in charge at Anfield in a bombshell interview on Friday morning.
Klopp and his backroom team helped guide Liverpool to six major trophies and ended the club's 30-year wait for a top-flight title.
But with Klopp's assistants also set for the exit door, next season will signal the beginning of a new era at the club.
Krawietz and Klopp have a long-standing history having worked together at Bundesliga outfit Mainz in 2001.
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The pair continued their working relationship at Borussia Dortmund before Krawietz followed Klopp to Anfield in 2015.
Unlike Krawietz, Lijnders was already at Liverpool upon Klopp's arrival, serving under previous manager Brendan Rodgers.
The Dutchman has gone on to become a vital member of Klopp's backroom team at Anfield, as the German's No 2.
Lijnders has made clear his ambitions of becoming a manager in his own right and is likely to pursue his ambition beyond the end of the current season.
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Meanwhile, Matos arrived at Anfield in 2019, providing the link between transitioning players from the academy to the first team.
A former assistant manager at FC Porto's B team, Matos has been responsible for a host of young players making the step up to the Reds' senior squad.
Klopp and his team will hope they can inspire Liverpool to one more trophy haul before they leave the club in the summer.
Liverpool hold a five-point lead at the top of the table with 17 games left to play. Klopp's side have already booked their place in the Carabao Cup final and are still involved in both the Europa League and FA Cup.