Tuchel has been out of work for nearly a year since leaving Borussia Dortmund at the end of last season, but his name has been strongly linked with the managerial position at the Emirates as pressure has increased on Wenger.
German newspaper Bild reports that Tuchel is already in talks with the Gunners hierarchy and could agree a move to north London, which would spell an end to Wenger's 22-year tenure at the club.
Most Arsenal fans have been in the "Wenger out" camp for a while now, with the Gunners currently sixth in the Premier League and 13 points off the top four.
Embarrassing defeats in the FA Cup and League Cup have cast further down on the 68-year-old's future, although he could yet redeem himself by winning the Europa League.
It has not been revealed why Tuchel turned down Bayern. The Bavarian club had lined him up as their first choice to replace Jupp Heynckes, who is expected to return to retirement after jumping back into management earlier this season.
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It may be because of Tuchel's ties to Dortmund, where he spent two seasons and won the DFB-Pokal. He was sacked after a third-place finish in his second year in charge, having fallen out with the club's hierarchy, who facilitated the sale of key players including Mats Hummels and Ilkay Gundogan.
A move to Arsenal would reunite Tuchel with former Dortmund stars Henrikh Mkhitaryan and Pierre-Emerick Aubameyang, both of whom joined the Gunners in January.