Pressure has been mounting on Arsene Wenger this season, with some supporters calling for the Gunners boss to step down, and Tuchel has been touted as a potential successor to the long-serving manager.
The Dortmund coach responded to the speculation on Friday, revealing that he was unaware of interest from the Premier League club and stressed that he was happy at the Westfalenstadion.
And the Bundesliga club's chief executive has also weighed in on the rumours, explaining that there has been no contact from the North London outfit.
"It is a fact that nobody from Arsenal called us. We're taking about completely fictional stuff here," Watzke told Sky.
"Some day in May we will sit down and analyze this season. He is still under contract here for another year. That's why I don't understand all the speculation."
Tuchel, 43, replaced Jurgen Klopp as Borussia Dortmund's head coach in 2015 and guided the team to a second-place finish that season.
BVB currently find themselves fourth in the Bundesliga and their hopes of closing the gap on the Bayern Munich and RB Leipzig were dealt a blow on Saturday following a 2-1 defeat to bottom-of-the-table Darmstadt.