Having scored 344 goals in 375 appearances for the German giants over the last eight seasons, the 33-year-old believes now is the right time to seek pastures new and he has expressed his desire to move to Camp Nou this summer.
Barca is understood to have recently tabled their first offer for the Poland international, but Marca claims that the bid has been rejected by Bayern.
The report adds that the Bayern also turned down a second offer from the Catalan giants on Friday worth around €35m (£30.1m) plus €5m (£4.3m) in add-ons, as they value their talisman at €50m (£43m).
The perennial Bundesliga winners are determined to keep hold of Lewandowski, who still has a year remaining on his contract at the Allianz Arena, but Barca remains 'cautiously optimistic' about recruiting the striker this summer.
The likes of Chelsea, Manchester United and Paris Saint-Germain have also been credited with an interest in Lewandowski, but it is thought that Barcelona would be the striker's preferred destination.