Kreuzer is sporting director at the Bundesliga outfit and claims the Toffees have expressed a willingness to do business.
With Roberto Martinez having snapped up Arouna Kone from former employers Wigan Athletic, he is said to be prepared to part with Jelavic.
The Croatia international did struggle at times last season, netting just eight goals in all competitions, but showed during his early days at Goodison Park what he is capable of - as he scored 11 times in 16 appearances after completing a move from Rangers in January 2012.
It is, however, possible that he has now been deemed surplus to requirements, and that Hamburg have him in their sights.
Kreuzer admits to having being an admirer of Jelavic for some time, but also concedes that his current employers may have to move players on before they can afford to put a deal in place.
He told Hamburger Morgenpost: "He is a great player. I know him very well. I wanted to get him out of Rapid Vienna and to Graz in 2010 before he went to Rangers. That transfer only just failed.
"We have been offered an opportunity. We will deal with it."
On financing a move, Kreuzer added: "Day in, day out, I talk to all the agents, but nothing has come up yet. If we manage that [to sell two or three players] we could work out if a loan or a payment in instalments would be possible."