The Bundesliga holders are suffering from an injury crisis in the heart of defence at present, as Dayot Upamecano withdrew from the France squad for October's fixtures with a hamstring problem.
Bayern confirmed Upamecano's diagnosis following a scan, and while it is unclear how long the Frenchman will be out for, he is expected to spend a few weeks on the treatment table.
In addition, Matthijs de Ligt has been struggling with a knee problem during the start of the 2023-24 season, and the Dutchman only began running without the ball again on Tuesday.
Eighteen-year-old protege Tarek Buchmann is also dealing with a torn muscle, leaving summer signing Kim Min-jae as Thomas Tuchel's only fit senior centre-back at present.
With the transfer window not reopening until January, Bayern must either hold out for another three months, look to their youth ranks or delve into the free agent market to address their rearguard shortages.
According to Bild, Bayern are now considering the latter option, and Tuchel is contemplating a reunion with 35-year-old Sokratis, whom he coached during their time at Dortmund.
The former Greece international has been out of the game since leaving Olympiacos upon the expiration of his contract in the summer, and he would be available to reinforce Bayern's backline immediately.
Sokratis rose to prominence during his five-year spell at Dortmund from 2013 to 2018, playing 198 times for the German giants, scoring 10 goals and winning one DFB-Pokal alongside two Super Cups.
The centre-back - who was named the 2016-17 Greece Player of the Year - is understood to possess an excellent relationship with Tuchel, who left Dortmund in acrimonious circumstances at the endo of the 2016-17 season.
Sokratis was subsequently sold to Arsenal for £13.9m in the 2018 summer window, and the 35-year-old managed six goals and two assists in 69 matches for the Gunners, winning one FA Cup before his contract was terminated in January 2021.
Earlier this year, the former Genoa man was apparently courted by Real Betis, who were keen to bring him to Spain as cover for Marc Bartra, but a deal ultimately collapsed.
As a result, Bayern will seemingly have a clear run at Sokratis, but the Bundesliga holders apparently want to see how De Ligt and Upamecano's issues heal over the next week before making any transfer decisions.
Tuchel's side also invited Jerome Boateng back to the club for training ahead of a potential short-term contract, but the Bavarians decided against adding him to their first-team squad.