Sporting director Arnesen admits he would welcome the opportunity to take Van der Vaart back to Germany four years after he departed the Imtech Arena.
The Holland international enjoyed three productive years in the Bundesliga between 2005 and 2008, before going on to take in spells at Real Madrid and Tottenham.
It has been suggested that he could be lured back to Hamburg this summer, with new Spurs boss Andre Villas-Boas apparently prepared to listen to offers.
There has been no official word from the White Hart Lane camp, though, and Arnesen admits there is little he can do until the player expresses a desire to move on.
"I can only say that he is a great player and one that knows Hamburg very well," Arnesen told Welt.
"I don't want to talk about it too much because Van der Vaart has a contract at Tottenham Hotspur until 2015.
"If I get a signal from his end that there might be something, things will be different.
"At the moment it is not practical. He is on holiday after the European Championship. In the next few weeks we will see what happens."
While looking to bring new additions into the Hamburg squad, Arnesen concedes that departures are also inevitable this summer.
He added: "There have been no offers yet but, after the European Championship, there will be interest in our players. There is always movement, and that is good for us."