The England international has been unable to play his way into Ange Postecoglou's good books and has failed to make a Premier League squad in 2023-24 so far.
Dier is also in the final year of his contract at the Tottenham Hotspur Stadium, and Spurs are hoping to garner a nominal fee for him this summer before he departs on a free transfer.
A part-exchange deal with Fulham for Tosin Adarabioyo has been mooted, but Tottenham are seemingly behind Monaco in the race for the ex-Manchester City academy product.
Postecoglou's former club Celtic has been touted as an alternative destination for Dier, but according to reporter Florian Plettenberg, Bayern have been presented with the chance to sign him multiple times.
A swoop for Dier has supposedly been a talking point for Bayern chiefs over the past few days, and the Bavarians may be open to a deal due to the 29-year-old's versatility.
Dier played as a defensive midfielder before transitioning to his current role, and Bayern are known to be searching for a new number six in the final few days of the transfer window.
In addition, centre-back acquisitions are also high up on Thomas Tuchel's agenda, as Benjamin Pavard is expected to complete a switch to Italian giants Inter Milan in the coming hours.
Dier is not the only name on Bayern's defensive shortlist, though, as moves for Chelsea's Trevoh Chalobah and Southampton's Armel Bella-Kotchap are also being considered.
However, Dier has supposedly been left out of Postecoglou's squad for their EFL Cup second-round clash with Fulham on Tuesday night, seemingly confirming that he is not in the Australian's thinking moving forward.
The former Sporting Lisbon youngster was a trusted member of Antonio Conte's back three last season, making 42 appearances across all competitions and coming up with two goals and one assist in the process.
Dier lost his place in the XI during the final few weeks of the campaign, although it was soon revealed that the England international had undergone surgery on a groin injury.
Since recovering, though, Dier has failed to break up the pairing of Cristian Romero and new signing Micky van de Ven, while Ben Davies and Davinson Sanchez are also ahead of him in the pecking order.
Should Dier fail to secure a move away in the coming days, he is expected to head elsewhere on a free transfer next year, although his hopes of a Euro 2024 call-up will diminish further if his playing situation does not improve.
The defender boasts 13 goals and 12 assists from 361 matches in a Spurs jersey since arriving in 2014, having previously played for Sporting and Everton at youth level.