With 12 goals for the orthern Germany club last season, the South Korean has caught the eye of many clubs around Europe with Liverpool and Tottenham very stongly linked, but Kreuzer has revealed that he is close to agreeing terms with Leverkusen.
"We think the transfer will go through in the next few days," he told Sky Deutschland.
"I expect Son to join Leverkusen."
A move for a reported 10 million euros could pave the way for Andre Schurrle's protracted move to Chelsea.
Leverkusen have said they will not let the Germany international go until they have found a suitable replacement, which now looks set to be 20-year-old Son.
With Son's contract due to expire in a year, now would be the last chance Hamburg would have of earning a significant sum for him.
"You have got to look at the sporting value of the player on the one side, and the economic value to the club on the other," added Kreuzer.