Leipzig have previously insisted that they will not consider selling their most prized asset ahead of 2022-23 after a goal-laden campaign.
The 24-year-old posted remarkable individual figures, contributing 31 goals and 14 assists from his 45 appearances in the Bundesliga and Europe.
However, according to Goal, Chelsea remained prepared to strike if Leipzig are unable to agree a new long-term contract with the Frenchman.
Although Nkunku still has two years remaining on his existing deal, Leipzig are aware that his value will drop if he heads into the final year of his contract.
From Chelsea's perspective, head coach Thomas Tuchel is likely to strengthen in all outfield areas, with the German seemingly open to parting ways with several of his current crop in the final third.
If reports are to be believed, Tuchel will also be provided with a £200m transfer warchest to close the gap to Manchester City and Liverpool. body check tags ::