The Croatian endured a difficult second season at Goodison and will be allowed to leave by new boss Roberto Martinez, according to the Bundesliga side's director.
The Bundesliga side is looking to strengthen its attacking options with Heung-Min Son leaving for Bayer Leverkusen this summer while attacker Artjom Rudnevs has limited competition up front beside him. And Hamburg is now ready to test if Jelavic is still needed on Merseyside next season or whether Martinez will allow the Croatia international to leave this summer.
"I have heard that Everton's new manager wants to sell him," Kreuzer 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.
"But we have to scrutinize whether it is financially possible."
Kreuzer admitted that the Bundesliga outfit will need to offload some fringe players before making a move for the 27-year-old, who is likely to cost around 7 million euros.
"Day in, day out, I talk to all the agents, but nothing has come up yet," Kreuzer said. "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."
Jelavic scored 11 goals in his first 16 appearances for the Toffees but was unable to recreate that form last season, with just eight goals in 43 appearances.