The South Korea international is one of Europe's most coveted youngsters at the moment, with Arsenal, Tottenham and Borussia Dortmund reportedly keeping close tabs on him.
His current contract with Hamburg expires at the end of next season and talks over an extension have so far been unsuccessful.
Should the situation remain unchanged, Arnesen is ready to part with the 20-year-old if the right offer comes along.
"Heung-min Son is under contract with our club and we are talking to him about signing a new contract," Arnesen told Bild
"Obviously we will have to sell him, if he does not sign a new deal with our club!"