Lijnders will follow manager Jurgen Klopp out of Anfield at the end of the season.
The Times says Lijnders could end up in Austria.
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RB Salzburg wants to hire the 41-year-old as new head coach this summer.
Salzburg has won the Austrian league ten years in a row.
With one round left in this season, Sturm Graz lead the league, two points ahead of Salzburg.