Arsene Wenger's long-standing tenure with the Premier League side has again come under the microscope after back-to-back defeats against Watford and Chelsea appeared to end the Gunners' title aspirations for another season.
The 67-year-old is out of contract at the end of the current campaign and a report by The Mirror suggested the Emirates Stadium hierarchy have compiled a four-man shortlist of potential successors amid the uncertainty, with Tuchel the primary target ahead of Juventus' Massimiliano Allegri, Bayer Leverkusen's Roger Schmidt and Monaco's Leonardo Jardim.
Speaking ahead of Saturday's Bundesliga trip to Darmstadt, Tuchel was keen not to further fuel the rumours.
"You know more than me," said the former Mainz boss when asked about Arsenal.
"I can't give any information about this issue because I don't know anything about it.
"I'm under contract with Dortmund and I'm happy here."
Dortmund are 12 points shy of leaders Bayern Munich in the Bundesliga and Tuchel insisted next Tuesday's Champions League trip to Benfica would have minimal bearing on his team selection versus bottom club Darmstadt.
"We will play with the best possible line-up," he said. "The Benfica match is not in our minds.
"The players who are physically fit will be part of the squad. There are not considerations to rest anyone.
"The favourites for the Darmstadt match are quite clear. In the past we had a tough time meeting these high expectations.
"We are always capable of creating chances. We should have decided recent games earlier."
The latest example of Dortmund's wastefulness came against Hertha Berlin in the DFB-Pokal in midweek, when they were held to a 1-1 draw before winning on penalties.
At the other end of the field, Tuchel has identified some cause for cheer, with former Barcelona centre-back Marc Bartra enjoying more impressive form after enduring a patchy start to life at Signal Iduna Park.
"Bartra has shown just how important he is for us in the past two games," the coach added, before reflecting on his earlier problems.
"His game is marked by aggressive defending. Sometimes it is difficult to stay patient against deep-lying teams."