The now 34-year-old is a free agent having left Real Madrid once his contract expired at the end of last season.
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Injury issues have seriously limited his game time over the past few seasons, making just 47 appearances across all competitions since 2023.
According to Sport BILD, Alaba could make a sensational return to the Bundesliga to help bolster a struggling Hamburg.
Hamburg currently sit rock bottom of the German top flight with three defeats, zero goals score, and a massive 12 conceded.
While a player with Alaba’s experience would doubtless prove valuable, financial constraints and the player’s injury record remain road blocks.