Financing a deal remains the biggest obstacle Hamburg must overcome before being able to welcome the Dutchman back.
"We have drawn up a target profile and Rafael van der Vaart would be an ideal fit," said Fink on Sport1.de.
"Any coach would be delighted to have him. Rafael is a very good player and he would be very interesting for Hamburg if we had the money to pay for him.
"And we are not lacking just a little, we are talking about a great deal of money."
Van der Vaart played for Hamburg between 2005 and 2008, scoring 29 goals in 74 appearances before joining Real Madrid.
He is just one of Hamburg's targets this summer with Fink "in constant dialogue with (director of sport) Frank Arnesen," as he said on the Bundesliga club's website.
"He is keeping me up to date, but we don't need to panic but rather only do what really makes sense for us," he said.
"We want to get a bit more experience, but that does not necessarily mean a player's age - (Lionel) Messi had enough experience when he was 24.
"I would have taken (Granit) Xhaka too because he has played in the Champions League.
"It is like (Otto) Rehhagel said: 'it doesn't matter whether young or old, what matters is good or not good.'"
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