The German outfit are looking to annul the Argentine's pre-agreement with Getafe that he signed five months ago after the player declared that he would like to join HSV
The German club's director Frank Arnesen told Hamburger Morgenpost last week that the move was a "done deal", before it emerged that Abraham had already signed a pre-contract with Getafe five months ago.
The Madrid side, keen to finalise the transfer, quickly proceeded to announce the arrival of the 25-year-old on their official website, claiming that he had penned a contract till 2016.
However, the Basel defender is said to relish a move to Hamburg after having a long discussion with coach Thorsten Fink.
"David has clearly made himself available to HSV," Abraham's agent Renato Cedrola said on Thursday.
"We are now actively trying to break the pre-agreement he had signed with Getafe CF."
Hamburg would have to pay a compensatory fee to Geta if Abraham was to move to the Imtech Arena, despite his contract with Basel running out this summer.