It is claimed the 44-year-old expects to become the new Arsenal manager, although Paris Saint-Germain are also said to be interested in him as a replacement for Unai Emery.
Germany and Bayern great Matthaus thinks Tuchel would be the right choice for Bayern but claims he has already been "in touch" with the Gunners.
"You know, I'm a journalist too, we have to make headlines every day," he told Omnisport following a match between Liverpool and Bayern legends at Anfield on Saturday.
"I think Thomas Tuchel can be the favourite, [the] ex-coach from Borussia Dortmund, but I know he's in touch with Arsenal and nobody knows what happens behind the doors."
Tuchel, who was Mainz head coach before taking over at Dortmund in 2015, left Signal Iduna Park last May, just three days after winning the DFB-Pokal.
He was said to have had an increasingly strained relationship with the club's hierarchy in his final weeks at the club, with CEO Hans-Joachim Watzke claiming he and sporting director Michael Zorc had been "worn out" by working with Tuchel.
He also f ell out with chief scout Sven Mislintat , who has since taken up the same role at Arsenal, but it is claimed the pair have buried the hatchet and are prepared to work together once again.