Nkunku scored 35 goals across all competitions last season, including a hat-trick in a Champions League group stage clash against Manchester City.
A former PSG player, the Ligue 1 champions will rival Chelsea in trying to sign Nkunku next summer. He made 55 league appearances for the Parisians before joining Leipzig in 2019.
Chelsea spent £250m on new talent in the summer transfer window, with Boehly keen to promise fans that he will not cut back on the spending under former owner Roman Abramovich. Raheem Sterling and Pierre-Emerick Aubameyang were added to the Blues’ forward line.
New boss Graham Potter, who replaced Thomas Tuchel at Stamford Bridge in September, faces his first Premier League match in charge on Saturday. Chelsea travel to London rivals Crystal Palace.