The 50-year-old is under increasing pressure amid a dreadful run of results at the German giants.
Bundesliga champions Bayern have lost their last three matches across all competitions, and Tuchel has been rumoured to have lost the dressing room.
A 3-0 defeat against league leaders Bayer Leverkusen was then followed up with a 1-0 loss against Lazio in the Champions League, before a 3-2 humbling at the hands of Bochum.
Bayern are now facing the prospect of their first campaign without winning a trophy since 2011-12, with Leverkusen eight points clear at the top of the Bundesliga.
talkSPORT understands West Ham are eyeing Tuchel as a potential replacement for David Moyes.
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Moyes' contact with the Hammers is up at the end of the current season, and the East London side could make a change.
The Scot has failed to lead his side to a single victory in 2024, and a number of fans have had enough.
They held banners in the away end with 'Moyes out' as they watched their team slump to a 2-0 defeat against Nottingham Forest last weekend.
West Ham have shipped 11 goals and failed to net in any of their last three Premier League matches, including their most recent 6-0 drubbing to Arsenal at home.
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Despite being an outside contender, there are hopes Tuchel could be persuaded back to London, having previously managed Chelsea.
Though he is not the only candidate to be linked with the job, with Steve Cooper another target, talkSPORT told.
Ex-Brighton and Chelsea boss Graham Potter, and former Wolves tactician Julen Lopetegui are also in the running.