Davies, whose contract at the Allianz Arena expires at the end of next season, is said to have verbally agreed to join La Liga leaders Real Madrid either this summer or on a free transfer in 2025.
Bayern have repeatedly tried and failed to tie Davies down to new terms, and the Bavarians will look to sell the Canada international in the upcoming window if it becomes clear that he will not pen a renewal.
Following the sale of Lucas Hernandez to Paris Saint-Germain, Davies's proposed exit would leave Raphael Guerreiro as Bayern's only senior left-back, while right-backs Noussair Mazraoui, Sacha Boey and Bouna Sarr have all struggled with injuries this season.
With Bayern seemingly fighting a losing battle to keep hold of Davies, the Bundesliga champions are now scoping out potential successors and have apparently earmarked AC Milan's Theo Hernandez as an ideal acquisition.
Now, the Daily Mail reports that Thomas Tuchel's men are also running the rule over Robertson, who is currently their number one pick to succeed Davies for the 2024-25 season and beyond.
The Scotland international has forged a reputation as one of Europe's best attacking full-backs since joining the Reds from Hull City in 2017, scoring nine goals and setting up 64 more in 282 matches for the club.
Robertson has set up 58 of those efforts in the Premier League, level with teammate Trent Alexander-Arnold as the defender with the most assists in the history of the competition, which he won in the 2019-20 season.
The 29-year-old has also achieved Champions League, FA Cup, Club World Cup, UEFA Super Cup, Community Shield and EFL Cup glory with Jurgen Klopp's side, winning his second title in the latter tournament on Sunday.
The 1-0 win over Chelsea at Wembley marked just Robertson's 15th appearance of the 2023-24 season, though, as he spent three months on the sidelines with a dislocated shoulder sustained on international duty.
Robertson has managed just one goal and one assist in all competitions during his disrupted 2023-24 campaign, but he remains an integral part of the furniture at Anfield and is under contract at the club until 2026.
As a result, Bayern supposedly accept that it will be a tall order to persuade Robertson to leave the Premier League leaders, but the Bavarians are aiming high and intend to replace Davies with a world-class option.
In spite of the fact that Robertson turns 30 next month, Bayern are allegedly of the view that he could replicate Davies's explosive showings down the left, and they are hopeful that the Scotsman will feel now is the time to embark on a new adventure.
In Robertson's absence, Joe Gomez performed well at left-back during the winter months, while Kostas Tsimikas and Luke Chambers - currently on loan at Wigan Athletic - will be other alternative options next season.