Sky Sports reports that Bayern are monitoring the Spain international and could explore a move during the winter transfer window.
The interest is linked to concerns over the future of Jamal Musiala and Michael Olise, two of the key attacking players in Vincent Kompany's squad. Bayern are considering contingency options should either player attract stronger interest from elsewhere.
Olmo has particular appeal because of his previous experience in Germany.
The Barcelona midfielder spent four seasons at RB Leipzig before returning to the club where he had started his youth career in 2024. His Bundesliga experience means Bayern already know the player well, while his ability to operate as a No 10 or from wider attacking positions fits the profile they are considering.
Olmo is currently wearing Barcelona's No 20 shirt and remains part of Hansi Flick's first-team plans. He has appeared in all seven of Barcelona's LaLiga matches this season, although most of those appearances have come from the bench.
The Bayern interest therefore comes at an interesting point in Olmo's Barcelona career.
He returned to Catalonia after Leipzig and played an important role in Barcelona's domestic treble-winning campaign, scoring 12 goals in 39 appearances despite injury problems.
A January departure would nevertheless be complicated.
Barcelona have no obvious reason to actively sell one of their attacking midfielders midway through the season, while Olmo remains under contract and is part of Flick's squad.
The reported Bayern interest is currently at the stage of the German club considering whether to make an approach rather than a confirmed offer.
For Bayern, the calculation is partly about preparation. Musiala and Olise remain central to their attacking plans, but growing outside interest in either player has encouraged the club to examine possible alternatives.
Olmo is one of the names now being considered.
And his familiarity with the Bundesliga, combined with his experience at the highest level with Barcelona and Spain, makes him a logical player for Bayern to investigate ahead of January.