The 61-year-old is currently out of work after being sacked by Roma last month, bringing his two-and-a-half years reign with the Serie A club to an end.
Mourinho was recently linked with a potential return to the Premier League, with one report claiming that the Portuguese has 'unfinished business' at Manchester United.
A possible move to Barcelona, who will have head coach Xavi stepping down at the end of the season, has also been mooted, but German news outlet Bild claims that Mourinho is keen to take over at Bayern Munich.
Mourinho has spent 24 years in management but he is yet to test himself in the Bundesliga, and journalist Christian Falk has revealed that the two-time Champions League winners is «learning German».
Speaking on BILD SPORT, Falk said: «I heard he's learning German. He has flirted with the office in the past. He would be ready.»
Mourinho's alleged interest in the Bayern hotseat comes at a time when current boss Tuchel has come under increased pressure as his side have fallen behind in the Bundesliga title race.
The Bavarian giants were comprehensively beaten 3-0 by leaders Bayer Leverkusen last weekend and have subsequently slipped five points behind Xabi Alonso's side in the top-flight standings.
Tuchel surprisingly used a three-man defence for the first time this season, a decision which ultimately backfired, while Matthijs de Ligt was allegedly left 'angry' by the 50-year-old's choice to leave him on the substitutes' bench.
Although supporter unrest is growing at the Allianz Arena, Bayern CEO Jan-Christian Dreesen has played down suggestions that Tuchel's job is at risk, telling Bild: «Nothing changes. We
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