Gunners boss Arsene Wenger is a long-term admirer of the French international and it has been alleged that he will launch another bid for the player during the summer transfer window.
However, according to Bild, they could have competition from Dortmund, who also face a fight to keep hold of Pierre-Emerick Aubameyang.
Lacazette has scored 29 goals in 38 appearances for Lyon this season, while he has 112 efforts to his name since 2009, but he has continued to stay loyal to his current employers.
However, he is likely to have options, and Dortmund will move for the 25-year-old should they receive a big-money offer for Aubameyang, who has been linked with a switch to England or Spain.
It may take a bid in the region of £40m for Lyon to be tempted into the sale of Lacazette.