The former Borussia Dortmund manager remains without a club following his exit from BVB last May.
Speculation from certain quarters suggests the 44-year-old has already turned down the chance to replace Juup Heynckes at Bayern Munich for the unique opportunity to become the Gunners' first new coach since 1996.
German legend Lothar Matthaus added to the speculation with his comments that Tuchel was his favourite for the post.
He told Omnisport: "Speak speculation, always, but I think Thomas Tuchel can be the favourite, ex-coach from Borussia Dortmund, but I know he’s the same in touch with Arsenal.
“Who knows what happens behind the doors.”
Tuchel is certainly highly rated, with Heynckes recently expressing his admiration by saying: "Thomas Tuchel has the quality to coach Bayern.
"I rate Thomas Tuchel. He has continued the progression from the youth teams at Mainz.
“That is the stairway to success that you must take, learning the correct approach and people skills.
“Under Tuchel, Borussia Dortmund played excellent football with a good system – all of today’s modern footballing elements were there for everyone to see.
“Tuchel’s side finished runners-up, won the DFB Pokal and played attractive football. I had fun watching BVB, that’s why I respect and rate him as a very good trainer.”
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