The 22-year-old has been part of Barcelona's senior squad since the 2021-22 season, but his progress has been interrupted by injuries and competition for places in midfield.
Gavi made 13 appearances in all competitions last season, registering one assist, while his involvement this term has so far amounted to eight matches, including two starts in LaLiga.
Despite his reduced playing time, he remains highly regarded and is under contract at Barcelona until the summer of 2030. Several major European clubs have been linked with him, including Liverpool, Paris Saint-Germain and Napoli.
However, his agent Iván de la Peña recently sought to play down speculation about a possible departure.
"I haven't negotiated with anyone. Gavi is staying at Barcelona," he told Tribuna.
The latest reports suggest Bayern are also monitoring developments. Journalist Juan Jesus claims the German champions are following the midfielder's situation closely, with Kompany understood to be an admirer.
The interest is not necessarily an indication that Bayern are preparing an immediate move. Instead, the club are reportedly keeping track of how Gavi's situation develops during the season, with a potential approach next summer also being considered.
Barcelona are not believed to be keen to sell one of their academy graduates, while the player himself is said to favour remaining at the Catalan club.
That leaves any prospective transfer dependent on a significant change in circumstances. Gavi would need to become available, and Barcelona would have to reconsider their position, before Bayern could turn their reported admiration into a concrete pursuit.
The midfielder has also established himself in the Spain set-up, scoring five goals in 32 senior international appearances.
Barcelona currently lead LaLiga after collecting 30 points from their opening 11 matches. Whether Gavi can force his way back into a more prominent role will be an important factor in determining whether the transfer speculation gathers momentum.