According to Fabrizio Romano, the two clubs have reached a verbal agreement, with only formalities and a medical still to be completed. The deal includes an option to make the move permanent for €20m.
Bah, who has won seven caps for Sierra Leone, opted for the Bavarian club having also had offers from clubs in Italy and Spain.
Manchester City signed the 20-year-old from Real Valladolid 18 months ago but he is yet to make a first-team appearance for the club, spending last season on loan at OGC Nice in Ligue 1, where he made 41 appearances in all competitions.
That followed an earlier loan spell at RC Lens during the second half of the 2024-25 campaign, giving Bah significant experience across two of Europe's top five leagues before he has even featured for his parent club.
Standing at 1.95m, Bah is regarded as a physically imposing defender with strong duel-winning ability, qualities that fit closely with what Augsburg were seeking to add to their backline before the transfer window closes.
His versatility and experience playing under different systems in Spain and France are seen as assets that should help him settle quickly into Bundesliga football. The move represents a fresh opportunity for Bah to continue his development away from Manchester City's crowded defensive options, with the loan expected to run for the full 2026-27 season.
Born in Freetown, Bah began his career with AIK Freetong before a loan move to Valladolid's B side in 2024 preceded his breakthrough into their first team, from where City signed him permanently.
Manchester City had reportedly set a guide price of around £15m plus add-ons for any club interested in a permanent deal this summer, with Atalanta among the sides said to have monitored his situation before Augsburg moved decisively to secure the loan.
Should the option to buy be triggered next summer, it would represent a significant return on a player who arrived in Manchester having made his name in the Spanish second tier only two years ago.