The Poland international has been linked with a move away from the Allianz Arena due to the German champions' alleged interest in Atletico Madrid striker Antoine Griezmann.
Lewandowski is contracted to Bayern until 2021, but the Bavarian giants are understood to be open to offers for the prolific striker, who has scored at least 40 goals in each of his three full seasons with the club.
German outlet Kicker reports that Premier League duo Man Utd and Chelsea are both interested in the 29-year-old, but could face competition from Paris Saint-Germain.
Chelsea are in the market for a new striker with Alvaro Morata's future at the club uncertain, while United are expected to splash the cash this summer in an attempt to close the gap on Manchester City.
Lewandowski scored 41 goals in 48 appearances for Bayern across all competitions this season.