The Paraguayan could return to the Bundesliga for a second spell after spending last season on loan at financially stricken Malaga, according to his representative
The 31-year-old, now without a club, spent eight years with Bayern Munich in Germany before eventually making a move to the Premier League to join Blackburn in 2007.
His success at Ewood Park earned him a transfer to Manchester City, but Santa Cruz failed to establish himself at the Etihad, going out on a succession of loan spells to the likes of Real Betis and Malaga in La Liga.
The player's agent, though, claims a move to Hamburg could now be on the cards. "The opportunity is there for HSV. Roque had a great time in Germany," Jan van Baal told Bild.
Santa Cruz has previously outlined his desire to remain at La Roselda with Malaga, but the cash-strapped Liga outfit may force the striker into a pay-cut for a deal to go through.
Malaga's financial problems mean they may have to sell some of their stars, such as reported City target Isco, but could retain others if they are willing to reduce their wages.
Santa Cruz scored eight goals in 30 appearances for the Andulucian outfit last season.