The 25-year-old has yet to agree on a new contract with Basel and could join Hamburg on a Bosman transfer.
Hamburg coach Thorsten Fink worked with Abraham during his previous spell as Basel boss.
“We have had a good round of talks with Hamburg,” Abraham’s agent Renato Cedrola told German newspaper Bild.
“We are in talks with several clubs, but Hamburg are a good club. We have yet to make a decision.”
He added: “Of course it is a big bonus both [Abraham and Fink] have already worked successfully with each other in the past.”