The 20-year-old has long been linked with a move away from HSV as both Borussia Dortmund and Leverkusen had earmarked the attacker as a valuable addition to their squad ahead of next season.
Leverkusen now seem to have beaten Dortmund to Son's signature and the deal could be completed in the upcoming days.
"I expect Son to make the move to Leverkusen. We think that the transfer will be a done deal in the next few days," Kreuzer told Sky Sport News.
Son joined Hamburg in the summer of 2008 and had since developed into one of the most sought-after players in the Bundesliga.
The South Korea international's current deal with HSV is due to expire in the summer of 2014, but Hamburg are ready to part ways with the versatile attacker for a transfer fee in the region of 10 million euros.
The imminent arrival of Son at Leverkusen could speed up the potential transfer of Andre Schurrle to Chelsea.
The Germany international has long been linked with a move to the Blues, but Leverkusen is reluctant to sell the 22-year-old until it has signed a replacement.
Meanwhile, Ajax defender Toby Alderweireld's agent, Soren Lerby, has admitted that the Belgium international would be open to a move to Leverkusen following reports that B04 are keen to sign the center back.
"I know that Toby is on Leverkusen's shortlist. The Bundesliga is a superb competition and Bayer would be a good club for Toby."
Alderweireld, 24, has a contract with Ajax until 2014, but could be available for about 6-8m euros.
Follow GOAL.COM on Twitter
- Borussia Dortmund
- Oliver Kreuzer