The Poland international has been linked with a move away from the German champions after previously declaring that his "era at Bayern is over" in a press conference with his national team last month.
Despite Lewandowski expressing a desire to leave the club, the Bayern hierarchy are determined to keep hold of the striker amid interest from Barcelona.
However, according to ESPN, Barcelona have ramped up their pursuit by making their first offer for the 33-year-old, whose contract is set to expire in 2023.
Bayern would be looking to secure over €40m (£34.3m) for the sale of Lewandowski, although Barcelona's offer is believed to fall short of that asking price.
Lewandowski helped Bayern claim their 10th consecutive Bundesliga title last season, scoring 35 goals in 34 league appearances for the Bavarians. body check tags ::