That is the claim from German football magazine Kicker, who claim he is on the verge of a deal with bosses at the Emirates.
Former Borussia Dortmund boss Tuchel is thought to have turned down the chance to manage Bayern Munich.
Bayern are looking for a new manager to take over from 72-year-old Jupp Heynckes, who came out of retirement when Carlo Ancelotti was sacked earlier this season.
But when Bayern set their sights on Tuchel he told them he wants to manage abroad, with the Premier League a likely destination.
Kicker say the 44-year-old will take over from Wenger at Arsenal come the end of the season.
Paris Saint-Germain and Chelsea have also been linked with Tuchel but it appears he is on his way to the Gunners.
Tuchel is well known by Arsenal’s new head of recruitment Sven Mislintat, with the pair having worked together at Dortmund.
Mislintat joined the Gunners last December, having left previous club Dortmund after clashing with Tuchel.
But Mislintat has assured club officials they could work well together in London.
German football legend Lothar Matthaus said: “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 has spent a season away from football since leaving Dortmund last summer.
The former Augsburg and Mainz manager replaced Jurgen Klopp as Dortmund boss in 2015 before leaving two years later.
A move Chelsea was also mooted, with the Blues set to part with Antonio Conte at the end of the season.
But Chelsea seem dead set on appointing ex-Barcelona manager Luis Enrique as their top man, with the Spaniard having already rejected the advances of PSG.
Wenger signed a new two-year contract at Arsenal last term, meaning the Frenchman would have to forego the last 12 months of his deal to let Tuchel take over, or be fired by the Arsenal board.
That second option appears unlikely considering his trusting relationship with Gunners owner Stan Kroenke.
Arsenal are on course to finish outside the Champions League spots for a second successive season.
However, victory in the Europa League would secure them passage to UEFA’s premier club competition next term.
