The 20-year-old, who has been linked to Liverpool and Arsenal, recently confirmed he was happy at the Bundesliga club but wants to see how Hamburg's season pans out before signing a new deal.
According to Son's agent Thies Bliemeister, preliminary discussions have been good but the South Korea international has not agreed to an improved offer of €2.8 million-a-season.
"We have been talking to HSV and the discussions have been good. However, there is no time pressure for us or HSV to get a deal sorted," he told Hamburger Abendblatt.
Son's current deal expires at the end of next season and Hamburg are hoping the forward would agree to an extension which would keep him at Imtech Arena until 2017.
If he snubs the improved deal, it is highly likely he will leave in the summer as Hamburg could risk losing him for free in 2014.