Chelsea remain keen to offload more players before the transfer window shuts on Friday.
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And Chalobah, 24, could be the latest star to make his Stamford Bridge exit.
Chalobah is out of favour at Stamford Bridge under Mauricio Pochettino, though he is currently sidelined due to a hamstring injury aggravated in training.
According to the Daily Mail, Bayern boss Thomas Tuchel is a huge admirer of Chalobah after working with him at Chelsea, when Tuchel handed him his debut.
With Benjamin Pavard expected to leave Munich in the coming days, Chalobah would be brought in to fill the vacant slot at full-back.
Although Chalobah’s versatility across a number of positions means he is ideal for plugging any gaps in the squad.
The Chelsea academy graduate also wants the move.
Bayern are not interested in a loan move for Chalobah and instead view him as a permanent addition.
His sale to Bayern would be a boost to Chelsea’s Financial Fair Play targets, with Chalobah showing up as pure profit on the books.
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Chalobah has made 63 appearances for Chelsea since emerging into the first team in 2021.
Elsewhere, Romelu Lukaku looks set to head back to Italy for a reunion with Jose Mourinho at Roma.
The Italian side are paying £8million for a season-long loan following breakthrough talks on Monday.
Lukaku is said to be taking a significant cut from his £325,000-a-week Chelsea wages.
There is understood to be a £37m buy option in the deal.
Despite pending exits, Chelsea remain in the market for a new attacker.
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