German newspaper Bild claim the Gunners have spoken to the Bundesliga side about a deal to bring the highly rated 43-year-old to north London at the end of the season.
Yesterday SunSport reported how Wenger has incredibly revealed he has already decided on his Arsenal future and will reveal all shortly.
The Gunners are now sixth in the Premier League and are in danger of missing out on Champions League football next season.
Tuchel took over at Borussia Dortmund after Jurgen Klopp left to take over at Liverpool.
If the offer exists - even if Tuchel rejects it - it would confirm that Wenger has chose to leave Arsenal after 21 years in charge.
"I'm still a very happy man, capable of being emotional with a special victory", Mourinho said.
Mourinho moaned that "nothing happens" when a manager pushes a referee, referring to Arsene Wenger's incident earlier this season.
The German publication suggested that Tuchel was contacted to take over from Arsene Wenger, but across a number of outlets this morning the message from Arsenal has been consistent that this is not the case.
Several high profile candidates have been linked with the Arsenal job, including Tuchel, Juventus manager Max Allegri, and outgoing Barcelona boss Luis Enrique.