The midfielder has been one of Leipzig's top performers this past season.
Nkunku is only 24, and won the Bundesliga Player of the Year award.
According to Goal.com, Nkunku is in contract negotiations with Leipzig, but may want to move on to a bigger club this summer.
Chelsea are seeking new attackers, as they look to solve their issue of a lack of goals.
Nkunku plays as a central attacking midfielder, but can also feature on either flank.