The 24-year-old has failed to impress at Atleti since his €70m move from Monaco in 2018.
Since then, his market value has fallen by a third and Diego Simeone rarely starts him in games.
Bayern are serious thinking about a loan offer for Lemar, due to his ability to play anywhere in the attacking midfield.
His French national team colleagues Corentin Tolisso, Lucas Hernandez, Kingsley Coman and Benjamin Pavard would help Lemar settle quickly.
Together with new boy Tanguy Kouassi, Bayern would then have a six-man group of Frenchmen.
RB Leipzig also like Lemar, but would find a deal difficult due to the costs involved.
An obstacle for Bayern is Atletico’s preference to sell Lemar rather than loan him out.
This complicates things for Bayern, who are more interested in loan deals at this stage of the window.
Bayern have made good use of the loan market recently, bringing in Philippe Coutinho, Ivan Perisic and Alvaro Odriozola on temporary deals last season.