Starsport revealed earlier this month that the Reds have made the Bayern Munich striker their top target ahead of the transfer window reopening.
The Polish international made his name under Jurgen Klopp at Borussia Dortmund and the Anfield chief is eager to work with him again.
But Klopp and co must now beat Arsenal to his signature.
The Mirror claimed today that Arsene Wenger wants to sign him this summer and is willing to shell out £50m to do so.
Lewandowski sparked speculation over his future last week by saying: "Maybe I’ll play in England or Spain one day.
"Thierry Henry has always been my idol, especially when he played for Arsenal. I watched a lot of his matches."
The 27-year-old has scored 44 goals in 51 games for club and country this season.
