Former Gunners boss Unai Emery held an interest in a reunion with the then-Paris Saint-Germain player during his time at the Emirates Stadium.
Nkunku eventually opted to move to Leipzig, where he has contributed six goals and 19 assists from 55 appearances in all competitions.
With the Frenchman having impressed in the Bundesliga and Champions League, Bild claims that Arsenal could contact Leipzig during the January transfer window.
However, Nkunku still has over three-and-a-half years remaining on his contract, leaving his club in a strong position with regards to his future.
Leipzig would likely demand in excess of £30m should Arsenal follow up their early interest.