The Chelsea academy graduate continues to be linked with a move away despite seeing a proposed switch to Inter Milan fall through earlier this summer.
Chalobah, who has made 63 appearances for the club, has found it difficult to nail down a consistent place in the senior side since making his debut in August 2021.
While Chalobah has missed the opening weeks of the season with a hamstring injury, he could find it difficult to force his way into Pochettino's starting lineup if he were to stay at the club.
The Chelsea boss can currently call upon Benoit Badiashile, Thiago Silva, Levi Colwill and summer addition Axel Disasi.
As a result, the Blues are open to the prospect of offloading Chalobah before the summer transfer window closes on Friday.
According to The Telegraph, Bayern boss Thomas Tuchel is keen to reunite with Chalobah after coaching the defender during his time as Chelsea head coach.
With Benjamin Pavard expected to join Italian giants Inter Milan, Bayern seemingly view Chalobah as a possible replacement for the Frenchman.
The report claims that Bayern are prioritising a permanent transfer and are currently in negotiations with Chelsea over a potential deal.
However, in a separate update, journalist Florian Plettenberg suggests that Bayern are pushing for a loan deal with an option to buy, while Chelsea are looking for a permanent sale.
With Lukaku set to join Roma in a temporary move, Chelsea will only be allowed to loan out one more player outside of England, having already seen Kepa Arrizabalaga, Gabriel Slonina, Angelo, Hakim Ziyech and David Datro Fofana leave the country on loan deals.
Chelsea are expected to use their last available slot to send Deivid Washington to Strasbourg, which will rule out the possibility of Chalobah leaving on loan.
While it remains to be seen whether the two clubs can agree a permanent transfer, Bayern have also identified AC Milan centre-back Pierre Kalulu as an alternative option.
However, the Italian side are reluctant to part ways with the centre-back, who is under contract until the summer of 2027.