The 33-year-old's contract with the Bavarian giants is due to expire in the summer of 2023, and he has allegedly informed the club of his desire to seek out a new challenge next year.
As a result, Lewandowski has unsurprisingly been linked with a switch to the Premier League, while Real Madrid have supposedly identified the Poland international as an ideal alternative to Erling Braut Haaland.
Manchester City have also been tipped to move for Lewandowski amid reports that they will not reignite their pursuit of Harry Kane, but Fichajes states that Liverpool are set to battle their top-flight rivals for his services.
The report adds Jurgen Klopp has specifically requested the signing of Lewandowski, who burst onto the scene under the German coach during their stint at Borussia Dortmund.
Lewandowski already boasts 10 goals from six games in all competitions this season, including a brace in Tuesday's 3-0 win over Barcelona in the Champions League.