The report comes from Bild who say that Arsenal have contacted Tuchel about possibly taking over.
However they also stress that Tuchel's preference is to stay with Dortmund, which would leave Juventus' Max Allegri as the main contender.
If the offer exists - even if Tuchel rejects it - it would confirm that Wenger has decided to leave Arsenal after 21 years in charge.
Wenger's contract is up at the end of the season but has a two-year extension on the table, leaving the decision over his future squarely with him.
Read the full article on eurosport.co.uk: Arsenal have approached Tuchel over manager's job - report