Lijnders joined Salzburg, the premier club in Austria, on a three-year deal in May after his tenure at Liverpool, where he served as Klopp's long-time assistant.
His dismissal comes just two weeks prior to Klopp assuming his new role overseeing Red Bull's struggling network of soccer clubs, which includes Salzburg.
In a joint statement, Salzburg CEO Stephan Reiter and sporting director Rouven Schröder expressed, "It has become evident that our performances in numerous matches have not met our expectations and objectives. We are convinced that a change in management is necessary to provide the team with a fresh impetus, despite our hopes for a turnaround until the very end."
Currently, Salzburg sits fifth in the Austrian league after 16 matches, trailing leader Sturm Graz by 10 points. Sturm Graz, the reigning champion, ended Salzburg's streak of 10 consecutive titles.
In the Champions League, Salzburg has managed to secure only one victory out of six matches, placing them 32nd in the 36-team standings, five points away from the qualification spots.
Next year, Salzburg will participate in the Club World Cup in the United States.
Lijnders concluded his tenure with a 3-0 victory against Austria Klagenfurt on Saturday, but the team remains in a precarious position as they approach the winter break.
Reiter and Schröder aim to appoint a new coach by January 3, when Salzburg resumes training after the break. Their next competitive match is scheduled for January 22 against Real Madrid in the Champions League.
Klopp will officially begin his role as head of global soccer at Red Bull on January 1, overseeing the international network of clubs, including Salzburg.
Salzburg is not the only Red Bull club facing difficulties; Leipzig has lost all six of its Champions League matches and has already been eliminated from the competition.